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Rectangles/209727: area of a rectangle is 243 m2. The height is nine less than 4 times the base. What is the perimeter?
1 solutions
Answer 162253 by drj(1380) About Me  on 2009-09-18 23:01:40 (Show Source):
You can put this solution on YOUR website!
Area of a rectangle is 243 m^2. The height is nine less than 4 times the base. What is the perimeter?

Step 1. Let x be the base and 4x-9 be the height

Step 2. Perimeter P means adding up the four sides of a rectangle.

Step 3. Then P=x%2Bx%2B4x-9%2B4x-9=10x-9

Step 4. Area=x*(4x-9)=243 or 4x^2-9x-243=0 or a quadratic equation.

Step 5. We can use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=4, b=-9 and c=-243

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-9x%2B-243+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-9%29%5E2-4%2A4%2A-243=3969.

Discriminant d=3969 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+3969+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+3969+%29%29%2F2%5C4+=+9
x%5B2%5D+=+%28-%28-9%29-sqrt%28+3969+%29%29%2F2%5C4+=+-6.75

Quadratic expression 4x%5E2%2B-9x%2B-243 can be factored:
4x%5E2%2B-9x%2B-243+=+4%28x-9%29%2A%28x--6.75%29
Again, the answer is: 9, -6.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-9%2Ax%2B-243+%29



Select the positive number x=9.


Step 6. Then P=x%2Bx%2B4x-9%2B4x-9=10x-9=10%2A9-9=81

Step 7. ANSWER: The perimeter is 81.


I just found this problem on 18 Sep 09, but I hope the above steps were helpful for review. Sorry about the late response.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Radicals/214168: Find the real solution(s) of the equation involving rational exponents
(x^2+6)^(2/3)=9
1 solutions
Answer 162250 by drj(1380) About Me  on 2009-09-18 22:49:51 (Show Source):
You can put this solution on YOUR website!
Find the real solution(s) of the equation involving rational exponents

%28x%5E2%2B6%29%5E%282%2F3%29=9

Step 1. Raise both sides of the equation by the power 3/2

%28%28x%5E2%2B6%29%5E%282%2F3%29%29%5E%283%2F2%29=9%5E%283%2F2%29 where 1/2 in the exponent is the square root and for this example sqrt%289%29=3

x%5E2%2B6=3%5E3=27

Step 2. Subtract 6 from both sides of the equation

x%5E2%2B6-6=27-6

x%5E2=21

x=sqrt%2821%29 or x=-sqrt%2821%29 ANSWER

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J





Radicals/214785: (x+6)^(1/2)=(x-9)

1 solutions
Answer 162248 by drj(1380) About Me  on 2009-09-18 22:40:00 (Show Source):
You can put this solution on YOUR website!
%28x%2B6%29%5E%281%2F2%29=%28x-9%29

Step 1. Square both sides of the equation

%28%28x%2B6%29%5E%281%2F2%29%29%5E2=%28x-9%29%5E2

x%2B6=x%5E2-18x%2B81

Step 2. Subtract x+6 from both sides of the equation to get a quadratic one.

x%2B6-%28x%2B6%29=x%5E2-18x%2B81-%28x%2B6%29

0=x%5E2-19x%2B75

Step 3. We can use the quadratic formula to solve this given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=-19 and c=75

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-19x%2B75+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-19%29%5E2-4%2A1%2A75=61.

Discriminant d=61 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--19%2B-sqrt%28+61+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+61+%29%29%2F2%5C1+=+13.4051248379533
x%5B2%5D+=+%28-%28-19%29-sqrt%28+61+%29%29%2F2%5C1+=+5.59487516204667

Quadratic expression 1x%5E2%2B-19x%2B75 can be factored:
1x%5E2%2B-19x%2B75+=+1%28x-13.4051248379533%29%2A%28x-5.59487516204667%29
Again, the answer is: 13.4051248379533, 5.59487516204667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B75+%29



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Step 2.

Polynomials-and-rational-expressions/214784: Hello, I need help with simplifying this rational expression:
x^2-100 over (x+10)^2
1 solutions
Answer 162243 by drj(1380) About Me  on 2009-09-18 22:15:11 (Show Source):
You can put this solution on YOUR website!
Simplify
%28x%5E2-100%29%2F%28x%2B10%29%5E2

Step 1. Rewriting the numerator using the difference of squares (x-10)(x+10)=x^2-10^2 and rewriting the denominator as follows yields,



Step 2. Canceling the (x+10) found in the numerator and denominator yields

%28x%5E2-100%29%2F%28x%2B10%29%5E2=%28x-10%29%2F%28x%2B10%29 ANSWER

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J


Proportions/214779: This question is from textbook intermediate algebra
My teacher wants use to write a narrative description of what you would do to simplify.

1. (16) power of 1/2 I know the answer is four b/c I did it in the calculator but how does it get that.

1 solutions
Answer 162242 by drj(1380) About Me  on 2009-09-18 21:49:30 (Show Source):
You can put this solution on YOUR website!
(16) power of 1/2 I know the answer is four b/c I did it in the calculator but how does it get that.

Step 1. The power of 1/2 means square root.

Step 2. Now we know 16+=+4%2A4=4%5E1%2A4%5E1=4%5E%281%2B1%29=4%5E2

16%5E%281%2F2%29=%284%5E2%29%5E%281%2F2%29=4%5E%282%2A%281%2F2%29%29=4%5E1=4 where in the exponent 2%2A%281%2F2%29=1 OR %284%5Em%29%5En=4%5E%28m%2An%29 where m=2 and n=1%2F2

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J



Linear-equations/214164: how do you graph how do you graph 1%2F2+%3C=t+%3C=+5%2F2
1 solutions
Answer 162236 by drj(1380) About Me  on 2009-09-18 21:36:12 (Show Source):
You can put this solution on YOUR website!
How do you graph how do you graph 1%2F2+%3C=t+%3C=+5%2F2

Step 1. You can think of the above inequality consist of two inequalities. That is,

2%2F3%3C=t and t%3C=5%2F2

Step 2. Then, on the number line we have

number_line%28600%2C+-10%2C10%2C+2%2F3%2C+5%2F2%29

Step 3. Now, the graph 2%2F3%3C=t is going from the red dot at 2/3 to the right pass the green dot to positive infinity or a positive large number.

Step 4. The graph t%3C=5%2F2 is going from the green dot at 5/2 to left pass the red dot to minus infinity or a negative large number.

Step 5. ANSWER. Finally, combining these two graphs as described above in Steps 3 and 4 will overlap with each other. The overlap and solution is between 2/3 and 5/2 or between the red and green dots as shown in the graph.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J













Trigonometry-basics/214777: what is:
x is less than pi/7? using interval notation.


1 solutions
Answer 162232 by drj(1380) About Me  on 2009-09-18 21:23:54 (Show Source):
You can put this solution on YOUR website!
What is:
x is less than pi%2F7? using interval notation.

I interpret your question as an inequality of

x%3Cpi%2F7
or
0%3Cx%3Cpi%2F7 if you want only positive angles.

I hope that was what you meant.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J





Expressions-with-variables/214774: Western State College is 18 years older than Southern State. Western is also 2.5 times as old as southern. how old is each? choices for southern state's age: 12,14,18
1 solutions
Answer 162230 by drj(1380) About Me  on 2009-09-18 21:20:09 (Show Source):
You can put this solution on YOUR website!
Western State College is 18 years older than Southern State. Western is also 2.5 times as old as southern. How old is each? choices for southern state's age: 12,14,18

Step 1. Let x be the age of Southern State, x+18 is the age of Western State College.

Step 2. 2.5x Western age is also 2.5 times as old as southern.

Step 3. x+18=2.5x as given by Steps 1 and 2.

Step 4. Subtract x to both sides of the equation in Step 3

x%2B18-x=2.5x-x

18=1.5x=3x%2F2

Step 4. Multiply 2/3 to both sides of the equation to get x

%282%2F3%29%2A18=%282%2F3%29%2A%283%2F2%29%2Ax

12=x

With x=12, then x+18=30 years old for Western

Step 5. ANSWER: Southern State's age is 12 years old and Western State's age is 30 years old.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/214764: Find slope-intercept form of the equation of the line with the following intercepts:
x-intercept: -7
y-intercept: 5
1 solutions
Answer 162226 by drj(1380) About Me  on 2009-09-18 21:07:44 (Show Source):
You can put this solution on YOUR website!
Find slope-intercept form of the equation of the line with the following intercepts:

x-intercept: -7
y-intercept: 5

Step 1. The slope-intercept form of the equation is given as y=mx+b where m is the slope and b is the y-intercept at point(0,5). For our example, b=5.

Step 2. To find the slope we use the x-intercept which means it occurs at point (-7,0) or x=-7 and y=0.

Step 3. Then

y=mx%2Bb=mx%2B5

0=m%2A-7%2B5

0=-7m%2B5

Add 7m to both sides of equation

7m=-7m%2B5%2B7m

7m=5

Divide 7 to both sides of equation

7m%2F7=5%2F7

m=5%2F7

Step 4. ANSWER: The equation of the line is y=5x%2F7%2B5}

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Miscellaneous_Word_Problems/214761: a certain number is increased by 8 ans that sum is divided by 2. the result is 6 1/4 . find the number.
1 solutions
Answer 162216 by drj(1380) About Me  on 2009-09-18 20:43:55 (Show Source):
You can put this solution on YOUR website!
A certain number is increased by 8 and that sum is divided by 2. The result is 6 1/4. Find the number.

Step 1. Let x be the number.

Step 2. %28x%2B8%29%2F2 that number is increased by 8 and that sum is divided by 2.

Step 3. %28x%2B8%29%2F2=25%2F4 where we converted 6%2B1%2F4=24%2F4%2B1%2F4=25%2F4

Step 4. Multiply 4 to get rid of denominators

4%2A%28x%2B8%29%2F2=4%2A25%2F4

2x%2B16=25

Step 5. Subtract 16 to both sides of equation

2x%2B16-16=25-16

2x=9

Step 6. Divide 2 to both sides of equation to get x

2x%2F2=9%2F2

x=9%2F2

Step 7. ANSWER: The number is 9/2.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Miscellaneous_Word_Problems/214759: sally has saved twice as much money as jon, jeremy has saved three times as much
money as jon. find the amount each person saved if the total savings is $180.00
1 solutions
Answer 162207 by drj(1380) About Me  on 2009-09-18 20:24:50 (Show Source):
You can put this solution on YOUR website!
Sally has saved twice as much money as Jon, Jeremy has saved three times as much
money as Jon. Find the amount each person saved if the total savings is $180.00


Step 1. Let x be the amount Jon saved, 2x be the amount Sally saved, and 3x be the amount Jeremy Saved.

Step 2. x+2x+3x=180 Sum of amount each person saved is 180 dollars.

Step 3. Solving yields

x%2B2x%2B3x=180

6x=180

6x%2F6=180%2F6 divide 6 to both sides of equation

x=30

2x=60

3x=90

30%2B60%2B90=180 Verify solution

Step 4. ANSWER: Jon saved $30, Sally saved $60, and Jeremy saved $90.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/214758: write the equation in slope-intercept form of the line satisfying:
m= 5/7, y-intercept (0,5)


1 solutions
Answer 162204 by drj(1380) About Me  on 2009-09-18 20:18:28 (Show Source):
You can put this solution on YOUR website!
Write the equation in slope-intercept form of the line satisfying:
m= 5/7, y-intercept (0,5)

The equation for the slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept at point (0,b).

For this example the slope m is 5/7 and b is 5. Then the equation of the line is

y=5x%2F7%2B5

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

test/214746: Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy?
1 solutions
Answer 162202 by drj(1380) About Me  on 2009-09-18 20:14:57 (Show Source):
You can put this solution on YOUR website!
Galina spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Galina buy?

Step 1. Let x be the number of 30 cents stamps.

Step 2. Let x-2 be the number of 20 cents stamps.

Step 3. Let 30x be the cost of buying x number of 30 cents stamps

Step 4. Let 20(x-2) be the cost of buying x-2 number of 20 cents stamps.

Step 5. 30x+20(x-2)=360 cents is the total cost of buying stamps.

Step 6. The following steps will solve the equation in Step 5:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=8.
  • Graphical form: Equation 30x%2B20%2A%28x-2%29=360 was fully solved.
  • Text form: 30x+20*(x-2)=360 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+30x%2B20%2A%28x-2%29=360+%29
    For tutors: simplify_cartoon( 30x+20*(x-2)=360 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 30%2Ax%2B20%2A%28x-2%29=highlight_red%28+360+%29.
Moved these terms to the left highlight_green%28+-360+%29
It becomes 30%2Ax%2B20%2A%28x-2%29-highlight_green%28+360+%29=0.
Look at 30%2Ax%2Bhighlight_red%28+20%2A%28x-2%29+%29-360=0.
Expanded term 20 by using associative property on %28x-2%29
It becomes 30%2Ax%2Bhighlight_green%28+20%2Ax+%29-highlight_green%28+20%2A2+%29-360=0.
Look at 30%2Ax%2B20%2Ax-highlight_red%28+20+%29%2Ahighlight_red%28+2+%29-360=0.
Multiplied numerator integers
It becomes 30%2Ax%2B20%2Ax-highlight_green%28+40+%29-360=0.
Look at 30%2Ax%2B20%2Ax-highlight_red%28+40+%29-highlight_red%28+360+%29=0.
Added fractions or integers together
It becomes 30%2Ax%2B20%2Ax%2Bhighlight_green%28+-400+%29=0.
Look at 30%2Ax%2B20%2Ax%2Bhighlight_red%28+-400+%29=0.
Removed extra sign in front of -400
It becomes 30%2Ax%2B20%2Ax-highlight_green%28+400+%29=0.
Look at highlight_red%28+30%2Ax+%29%2Bhighlight_red%28+20%2Ax+%29-400=0.
Eliminated similar terms highlight_red%28+30%2Ax+%29,highlight_red%28+20%2Ax+%29 replacing them with highlight_green%28+%2830%2B20%29%2Ax+%29
It becomes highlight_green%28+%2830%2B20%29%2Ax+%29-400=0.
Look at %28highlight_red%28+30+%29%2Bhighlight_red%28+20+%29%29%2Ax-400=0.
Added fractions or integers together
It becomes %28highlight_green%28+50+%29%29%2Ax-400=0.
Look at highlight_red%28+%28highlight_red%28+50+%29%29%2Ax+%29-400=0.
Remove unneeded parentheses around factor highlight_red%28+50+%29
It becomes highlight_green%28+50+%29%2Ax-400=0.
Look at highlight_red%28+50%2Ax-400+%29=0.
Solved linear equation highlight_red%28+50%2Ax-400=0+%29 equivalent to 50*x-400 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=8.

Universal Simplifier and Solver


Done!



With x=8, then x-2=6

Step 7 The number of 30 cents stamps is 8 and the number of 20 cents stamps is 6.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Expressions-with-variables/214757: A clown weighs 60lb more than a trapeze artist. The trapeze artist weighs two thirds as much as the clown. How much does each weigh? Choice for the weight of the trapeze artist: 110, 120, 125.
1 solutions
Answer 162201 by drj(1380) About Me  on 2009-09-18 20:08:46 (Show Source):
You can put this solution on YOUR website!
A clown weighs 60lb more than a trapeze artist. The trapeze artist weighs two thirds as much as the clown. How much does each weigh? Choice for the weight of the trapeze artist: 110, 120, 125.

Step 1. Let x be the weight of the trapeze artist and x+60 is the weight of the clown.

Step 2. x=2%28x%2B60%29%2F3 Trapeze artist weights two thirds as much as the clown.

Step 3. Solving equation in Step 2 yields

x=2%28x%2B60%29%2F3

Multiply by 3 to both sides of equation to get rid of denominator

3x=2%28x%2B60%29=2x%2B120

Subtract 2x to both sides of equation

3x-2x=2x%2B120-2x

x=120

Then weight to clown is

x%2B60=180

Step 4. Weight of trapeze artist is 120 pounds and weight of clown is 180 pounds.

Step 5. ANSWER: Trapeze artist weighs 120 pounds.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Travel_Word_Problems/214753: Electricity travels at 186,000 mi/s. How far does electricity travel in
200 ps? Give your answer in inches.
I think the answer is 3. I know it is less than 4 inches. What I am looking for is the formula I need to use. What is listed in the math book does not cover ps and is very confusing. Thanks in advance.
1 solutions
Answer 162193 by drj(1380) About Me  on 2009-09-18 19:24:08 (Show Source):
You can put this solution on YOUR website!
Electricity travels at 186,000 mi/s. How far does electricity travel in
200 ps? Give your answer in inches.

Step 1. 200 picoseconds = 200%2A10%5E%28-12%29 seconds = 2%2A10%5E%28-10%29 seconds

Step 2. (186,000 miles/sec)*(5280 feet/mile)*(12 inch/feet)*2*10^(-10) sec = 2.357 inches.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J


Expressions-with-variables/214752: This question is from textbook Algebra: Structure and Method Book 1
Two numbers differ by 57. Their sum is 185. Find the numbers. Choices for the smaller number: 29,30, 33.
1 solutions
Answer 162191 by drj(1380) About Me  on 2009-09-18 19:05:16 (Show Source):
You can put this solution on YOUR website!
Two numbers differ by 57. Their sum is 185. Find the numbers. Choices for the smaller number: 29,30, 33.

Step 1. Let x be one number and y be the other number.

Step 2. Then based on the problem statement we have the following.

x-y=57 Equation A

x%2By=185 Equation B

Add Equations A and B to get

2x=242

x=121

Then y=185-121=64

ANSWER is 64 but it does not appear in your solutions. May need to double check to see if the above problem statement is correct.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Numbers_Word_Problems/214750: One-sixth of the smallest of three consecutive even integers is three less than one-tenth the sum of the other even integers. Find the integers.
1/6x +3 = 1/10 (x+2)+(x+4)
1/6x +3 = 1/10 (2x+6)
1/6x +3 -3 = 1/10 (2x+3)
here is where I lose it, do not understand what to do with the fractions.
1 solutions
Answer 162190 by drj(1380) About Me  on 2009-09-18 18:57:02 (Show Source):
You can put this solution on YOUR website!
One-sixth of the smallest of three consecutive even integers is three less than one-tenth the sum of the other even integers. Find the integers.

Step 1. Let x be an even integer, x+2 and x+4 be the next two consecutive integers.

Step 2. x+2+x+4 is the sum of the two even integers or 2x+6
Step 3. (2x+6)/10 is one-tenth of the sum of the other even integers.

Step 4. x/6 is one-sixth of the smallest even itneger

Step 5. x%2F6=%282x%2B6%29%2F10-3 as given by the problem statement.

Step 6 Multiply 60 to both sides of the equation to get rid of the fractions.

60%2Ax%2F6=60%2A%28%282x%2B6%29%2F10-3%29

10x=6%2A%282x%2B6%29-180

10x=12x%2B36-180

10x=12x-144

Add 144-10x to both sides

10x%2B144-10x=12x-144%2B144-10x

2x=144

x=72

Step 7. The numbers are 72, 74 and 76.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/214749: given the function K(r)=10r+5 find each of the following
K(4)=
K(-9)=
K(6.7)=
1 solutions
Answer 162188 by drj(1380) About Me  on 2009-09-18 18:39:28 (Show Source):
You can put this solution on YOUR website!
given the function K(r)=10r+5 find each of the following

K%284%29=10%2A4%2B5=45

K%28-9%29=10%2A%28-9%29%2B5=-90%2B5=-85

K%286.7%29=10%2A%286.7%29%2B5=67%2B5=72

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J


Linear_Equations_And_Systems_Word_Problems/214747: Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?
1 solutions
Answer 162187 by drj(1380) About Me  on 2009-09-18 18:37:05 (Show Source):
You can put this solution on YOUR website!
Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?

Step 1. Let x number of small cups sold.

Step 2. Let y number of large cups sold.

Step 3. Let 1.25x be the cost of small cups sold.

Step 4. Let 2.50x be the cost of large cups sold.

Step 5. Then we have the following relationships:

x%2By=155 where the total number of cups sold is 155

1.25x%2B2.50y=265 where the total cost of cups sold is $265.

Step 6. The following steps will solve the system of equations in Step 5.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 1*y to the right, we get:
1%2Ax+=+155+-+1%2Ay, or x+=+155%2F1+-+1%2Ay%2F1. Substitute that
into another equation:
1.25%2A%28155%2F1+-+1%2Ay%2F1%29+%2B+2.5%5Cy+=+265 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



Step 7. The number of small cups sold is 98 and the number of large cups sold is 57.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J


Percentage-and-ratio-word-problems/214734: Your friend paid $11.70 for a bag of popcorn at the movie theater. This amount was 52% of the total amount your friend spent at the theater. How much money did your friend spend (in dollars)?

1 solutions
Answer 162185 by drj(1380) About Me  on 2009-09-18 18:24:42 (Show Source):
You can put this solution on YOUR website!
Your friend paid $11.70 for a bag of popcorn at the movie theater. This amount was 52% of the total amount your friend spent at the theater. How much money did your friend spend (in dollars)?

Step 1. 52%=0.52 by definition of percent.

Step 2. Let Total Cost = T

Step 3. Cost of popcorn = $11.70 = 0.52*T since 52% of Total Cost or T=11.70/.52= 22.50

Step 4. The total cost his friend spent was $22.50.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Percentage-and-ratio-word-problems/214735: A car salesperson earns a 12.5% commission on every car sold. The sales−person sells a car for $17100. What is the commission (in dollars)?

1 solutions
Answer 162184 by drj(1380) About Me  on 2009-09-18 18:19:33 (Show Source):
You can put this solution on YOUR website!
A car salesperson earns a 12.5% commission on every car sold. The sales person sells a car for $17100. What is the commission (in dollars)?

Step 1. 12.5%=0.125 Definition of percent.

Step 2. Multiply car cost by percent of commission will to get commission in dollars
17100%2A0.125=2137.50

Step 3. ANSWER: The commission is $2137.50.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/214740: 8x+3y=34
-5x+y=27
1 solutions
Answer 162181 by drj(1380) About Me  on 2009-09-18 18:15:47 (Show Source):
You can put this solution on YOUR website!
8x+3y=34
-5x+y=27

The following will solve the system of equations using substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++8%5Cx+%2B+3%5Cy+=+34%2C%0D%0A++++-5%5Cx+%2B+1%5Cy+=+27+%29%0D%0A++We'll use substitution. After moving 3*y to the right, we get:
8%2Ax+=+34+-+3%2Ay, or x+=+34%2F8+-+3%2Ay%2F8. Substitute that
into another equation:
-5%2A%2834%2F8+-+3%2Ay%2F8%29+%2B+1%5Cy+=+27 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Linear-systems/214742: 5x+5y=-11
7x-2y=17
1 solutions
Answer 162179 by drj(1380) About Me  on 2009-09-18 18:14:11 (Show Source):
You can put this solution on YOUR website!
5x+5y=-11
7x-2y=17

The following will solve the system of equations using substitution:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++5%5Cx+%2B+5%5Cy+=+-11%2C%0D%0A++++7%5Cx+%2B+-2%5Cy+=+17+%29%0D%0A++We'll use substitution. After moving 5*y to the right, we get:
5%2Ax+=+-11+-+5%2Ay, or x+=+-11%2F5+-+5%2Ay%2F5. Substitute that
into another equation:
7%2A%28-11%2F5+-+5%2Ay%2F5%29+%2B+-2%5Cy+=+17 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
Linear-systems/214739: `6x+2y=8
-3x+y=20

1 solutions
Answer 162178 by drj(1380) About Me  on 2009-09-18 18:12:35 (Show Source):
You can put this solution on YOUR website!
6x%2B2y=8 Equation A
-3x%2By=20 Equation B

Step 1. Multiply Equation B by 2 and Add the two equations.

-3x%2By=20
-6x%2B2y=40
6x%2B2y=8
Step 2. This yields

4y=48 or y=12

Step 3. Substitue y=12 into equation A or B. Here's for Equation A

6x%2B2%2A12=8

6x=-16

x=-16%2F6=-8%2F3

Step 4. ANSWER: The solution is x=-8/3 and y=12.

As a check here's the solution using SUBSTITUTION:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++6%5Cx+%2B+2%5Cy+=+8%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+20+%29%0D%0A++We'll use substitution. After moving 2*y to the right, we get:
6%2Ax+=+8+-+2%2Ay, or x+=+8%2F6+-+2%2Ay%2F6. Substitute that
into another equation:
-3%2A%288%2F6+-+2%2Ay%2F6%29+%2B+1%5Cy+=+20 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



The results are the same as before.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Functions/214733: I have to find the composition of functions! I did 16 problems already with no problem but can't figure this one out.
g(x)=(2x)^1/2 f(x)=x^2+1 find (Fog)(x)

I would welcome any help!!!!!
1 solutions
Answer 162173 by drj(1380) About Me  on 2009-09-18 18:03:52 (Show Source):
You can put this solution on YOUR website!
I have to find the composition of functions! I did 16 problems already with no problem but can't figure this one out.
g(x)=(2x)^1/2 and f(x)=x^2+1. Then find (Fog)(x)=F(g(x))

Step 1. Substitute g(x)=2x^1/2 into f(x) as follows

Step 2. f%282x%5E%281%2F2%29%29=%282x%5E%281%2F2%29%29%5E2%2B1=2x%5E%28%281%2F2%29%2A2%29%2B1=2x%2B1

Step 3. ANSWER: Fog(x)=F(g(x))=2x+1

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Number-Line/214729: wat is 29-58? inoe its -29 but i want to know the steps on how to get to get -29

1 solutions
Answer 162172 by drj(1380) About Me  on 2009-09-18 17:55:34 (Show Source):
You can put this solution on YOUR website!
What is 29-58? I know it's -29 but I want to know the steps on how to get to get -29.


29-58=29+(-58)=-29. Where we used the additive inverse of 58.

Think of walking 29 forward steps and then 58 backward steps. The net result is that you went 29 steps backwards from where you started.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J


Linear-systems/214731: 6x+2y=8
-3x+y=20
8x+3y=34
-5x+y=27

1 solutions
Answer 162171 by drj(1380) About Me  on 2009-09-18 17:51:15 (Show Source):
You can put this solution on YOUR website!
Using SUBSTITUTION, the following will solve the system of equations given as

6x%2B2y=8
-3x%2By=20

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++6%5Cx+%2B+2%5Cy+=+8%2C%0D%0A++++-3%5Cx+%2B+1%5Cy+=+20+%29%0D%0A++We'll use substitution. After moving 2*y to the right, we get:
6%2Ax+=+8+-+2%2Ay, or x+=+8%2F6+-+2%2Ay%2F6. Substitute that
into another equation:
-3%2A%288%2F6+-+2%2Ay%2F6%29+%2B+1%5Cy+=+20 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



Using SUBSTITUTION, the following will solve the system of equations given as

8x+3y=34
-5x+y=27

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++8%5Cx+%2B+3%5Cy+=+34%2C%0D%0A++++-5%5Cx+%2B+1%5Cy+=+27+%29%0D%0A++We'll use substitution. After moving 3*y to the right, we get:
8%2Ax+=+34+-+3%2Ay, or x+=+34%2F8+-+3%2Ay%2F8. Substitute that
into another equation:
-5%2A%2834%2F8+-+3%2Ay%2F8%29+%2B+1%5Cy+=+27 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
Numbers_Word_Problems/214726: What are the four consecutive even integers that equal 308?
1 solutions
Answer 162170 by drj(1380) About Me  on 2009-09-18 17:43:26 (Show Source):
You can put this solution on YOUR website!
What are the four consecutive even integers that equal 308?

Step 1. Let n be an even integer, n+2, n+4, and n+6 be the next three consecutive integers.

Step 2. Then n+n+2+n+4+n+6=308 as given by the problem statement where the sum of the four consecutive integers equal to 308.

Step 3. The following steps will solve the equation in Step 2:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: n=74.
  • Graphical form: Equation n%2Bn%2B2%2Bn%2B4%2Bn%2B6=308 was fully solved.
  • Text form: n+n+2+n+4+n+6=308 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B2%2Bn%2B4%2Bn%2B6=308+%29
    For tutors: simplify_cartoon( n+n+2+n+4+n+6=308 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2Bn%2Bhighlight_red%28+2+%29%2Bn%2Bhighlight_red%28+4+%29%2Bn%2Bhighlight_red%28+6+%29=308.
Added fractions or integers together
It becomes n%2Bn%2Bhighlight_green%28+12+%29%2Bn%2Bn=308.
Look at n%2Bn%2Bhighlight_red%28+12+%29%2Bn%2Bn=308.
Moved 12 to the right of expression
It becomes n%2Bn%2Bn%2Bn%2Bhighlight_green%28+12+%29=308.
Look at .
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%2B1%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%2B1%2B1%29%2An+%29%2B12=308.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2An%2B12=308.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2An+%29%2B12=308.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2An%2B12=308.
Look at 4%2An%2B12=highlight_red%28+308+%29.
Moved these terms to the left highlight_green%28+-308+%29
It becomes 4%2An%2B12-highlight_green%28+308+%29=0.
Look at 4%2An%2Bhighlight_red%28+12+%29-highlight_red%28+308+%29=0.
Added fractions or integers together
It becomes 4%2An%2Bhighlight_green%28+-296+%29=0.
Look at 4%2An%2Bhighlight_red%28+-296+%29=0.
Removed extra sign in front of -296
It becomes 4%2An-highlight_green%28+296+%29=0.
Look at highlight_red%28+4%2An-296+%29=0.
Solved linear equation highlight_red%28+4%2An-296=0+%29 equivalent to 4*n-296 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=74.

Universal Simplifier and Solver


Done!



Step 4. The integers are: 74, 76, 78, and 80.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J


Proportions/214724: A sofa is 6 feet long. In a scale drawing, the sofa is 3 inches long. Find the scale of the drawing without units.

1 solutions
Answer 162167 by drj(1380) About Me  on 2009-09-18 17:36:23 (Show Source):
You can put this solution on YOUR website!
A sofa is 6 feet long. In a scale drawing, the sofa is 3 inches long. Find the scale of the drawing without units.

Given the sofa is 6 feet long, the scale drawing 3 inches long. Let s be the scale ratio without units. Note 1 foot = 12 inches then 1/4 feet is 3 inches.

I'll give two scale factors depending how you want the answer.

APPROACH 1. Hence, s=6/3 or s=1/2. This means at if the length is 3 feet then the scale drawing is 3*(1/2)=1.5 inches.

So this is a scale conversion of feet/inches (so this is not unitless)

APPROACH 2. We can change the scale factor by changing the denominator to 1/4=3 inches. So

s=6/(1/4)=24. So the scaling is 24 to 1. So 6 feet/24= 1/4 feet or 3 inches in the scale drawing. So this is unitless scale s since the conversion is feet/feet.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J






Graphs/214716: graph the system of unequalities
x+2y<6
2x+y<6
x>0
y>0
1 solutions
Answer 162163 by drj(1380) About Me  on 2009-09-18 17:21:23 (Show Source):
You can put this solution on YOUR website!
Graph the system of unequalities

x+2y<6
2x+y<6
x>0
y>0


Graph of x%2B2y%3C6

Solved by pluggable solver: Plot Any Inequality
Graphing function x%2B2y%3C6:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B2y%3C6+%29



Graph of 2x%2By%3C6

Solved by pluggable solver: Plot Any Inequality
Graphing function 2x%2By%3C6:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2By%3C6+%29



Graph of x%3E0

Solved by pluggable solver: Plot Any Inequality
Graphing function x%3E0:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%3E0+%29



Graph of y%3E0%29


Solved by pluggable solver: Plot Any Inequality
Graphing function y%3E0:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3E0+%29




I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Numbers_Word_Problems/214714: The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number. This question is on a handout my child brought home. There is no ISBN
1 solutions
Answer 162159 by drj(1380) About Me  on 2009-09-18 17:00:42 (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 120. The second number is 8 less than the first number, and the third is 4 more than the first number

Step 1. Let x be the first number

Step 2. Let x-8 be the second number since it's 8 less than the first number

Step 3. Let x+4 be the third number since it's 4 more than the first number

Step 4. Then, x+x-8+x+4=120 since we're given the sum of three numbers is 120.

Step 5. The following will solve the above equation in step 4.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=41.3333333333333.
  • Graphical form: Equation x%2Bx-8%2Bx%2B4=120 was fully solved.
  • Text form: x+x-8+x+4=120 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2Bx-8%2Bx%2B4=120+%29
    For tutors: simplify_cartoon( x+x-8+x+4=120 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2Bx-highlight_red%28+8+%29%2Bx%2Bhighlight_red%28+4+%29=120.
Added fractions or integers together
It becomes x%2Bx%2Bhighlight_green%28+-4+%29%2Bx=120.
Look at x%2Bx%2Bhighlight_red%28+-4+%29%2Bx=120.
Moved -4 to the right of expression
It becomes x%2Bx%2Bx%2Bhighlight_green%28+-4+%29=120.
Look at x%2Bx%2Bx%2Bhighlight_red%28+-4+%29=120.
Removed extra sign in front of -4
It becomes x%2Bx%2Bx-highlight_green%28+4+%29=120.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+x+%29%2Bhighlight_red%28+x+%29-4=120.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+x+%29 replacing them with highlight_green%28+%281%2B1%2B1%29%2Ax+%29
It becomes highlight_green%28+%281%2B1%2B1%29%2Ax+%29-4=120.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2Ax-4=120.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-4=120.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-4=120.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-4=120.
Look at 3%2Ax-4=highlight_red%28+120+%29.
Moved these terms to the left highlight_green%28+-120+%29
It becomes 3%2Ax-4-highlight_green%28+120+%29=0.
Look at 3%2Ax-highlight_red%28+4+%29-highlight_red%28+120+%29=0.
Added fractions or integers together
It becomes 3%2Ax%2Bhighlight_green%28+-124+%29=0.
Look at 3%2Ax%2Bhighlight_red%28+-124+%29=0.
Removed extra sign in front of -124
It becomes 3%2Ax-highlight_green%28+124+%29=0.
Look at highlight_red%28+3%2Ax-124+%29=0.
Solved linear equation highlight_red%28+3%2Ax-124=0+%29 equivalent to 3*x-124 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=41.3333333333333.

Universal Simplifier and Solver


Done!



With x=41.33333... or x=124%2F3

x-8=124%2F3-24%2F3=100%2F3

x%2B4=124%2F3%2B12%2F3=136%2F3

So the numbers are 124%2F3, 100%2F3, and 136%2F3 Note these numbers add up to 120.
I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J