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Recent problems solved by 'Stitch'

Stitch answered: 351 problems
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Proportions/711700: YMy question is;
Lawrence High prevailed in Saturdays track meet with the help of 20 individual-event placers earning a combined 68 points. A first place finish earns 5 points, a second place earns 3 points, and third place earns 1 point. Lawrence had s strong second-place showing, with as many second-place finishes as first and third place finishers combined. (hint: the third equation will be as: y=x+z)
1 solutions

Answer 437555 by Stitch(352) on 2013-02-07 12:27:46 (Show Source):

You can put this solution on YOUR website!
Since you used XYZ in the write up I will continue that.
Let X = number of first place finishers
Let Y = number of second place finishers
Let Z = number of third place finishers
Below are the equations that you need to set up to solve the problem. Behind each equation is the part of the text where the equation was made from.
Equation 1: X+%2B+Y+%2B+Z+=+20

"with the help of 20 individual-event placers"
Equation 2: 5X+%2B+3Y+%2B+Z+=+68

"earning a combined 68 points. A first place finish earns 5 points, a second place earns 3 points, and third place earns 1 point."
Equation 3: Y+=+X+%2B+Z

"with as many second-place finishes as first and third place finishers combined."
------------------------------------------------------------
Equation 3 is already solved for 1 varible.
Plug (X + Z) into equation 1 for Y. You can then solve for one of the other variables.
Equation 1: X+%2B+Y+%2B+Z+=+20

Combine like terms
2X+%2B+2Z+=+20

I will solve for Z.
Pull a 2 from the left sides of the equation.
2%2A%28X+%2B+Z%29+=+20

Divide both sides by 2
X+%2B+Z+=+10

Subtract X from both sides
Z+=+10+-+X

Now we have all the variables in terms of X.
Substitute these values into equation 2 and solve for X
Equation 2: 5X+%2B+3Y+%2B+Z+=+68

5X+%2B+3%2A%28Z+%2B+X%29+%2B+%2810+-+X%29+=+68

Multiply the 3 through.
5X+%2B+3Z+%2B+3X+%2B+10+-+X+=+68

Combine like terms.
7X+%2B+3Z+%2B+10+=+68

Subtract 10 from both sides
7X+%2B+3Z+=+58

We need to get rid of the Z, substitute the (10-X) in for Z.
7X+%2B+3%2A%2810+-+X%29+=+58

Multiply the 3 through
7X+%2B+30+-+3X+=+58

Combine like terms.
4X+%2B+30+=+58

Subtract 30 from both sides
4X+=+28

Divide both sides by 4
highlight%28X+=+7%29

Now solve for Y & Z by using 7 for X
---------------------------
From earlier: Z+=+10+-+X

---------------------------
Equation 3: Y+=+X+%2B+Z

Sequences-and-series/711687: Is there a value of n such that n^2 + n + 1 is a multiple of 5?
1 solutions

Answer 437552 by Stitch(352) on 2013-02-07 12:06:34 (Show Source):

You can put this solution on YOUR website!

Yes, there are values of n that produce multiples of 5. On the graph lines are drawn when Y=5, Y=10, Y=15 & Y=20. However the values of n that produce a multiple of 5 may not be whole numbers.
-------------------------------
For example we can solve for what value of n makes the equation equal 10.
n%5E2+%2B+n+%2B+1+=+10

Subtract 10 from both sides
n%5E2+%2B+n+-+9+=+0

Now we can use the quadratic equation to solve for n

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation an%5E2%2Bbn%2Bc=0

(in our case 1n%5E2%2B1n%2B-9+=+0

) has the following solutons:

n%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

.

Discriminant d=37 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+37+%29%29%2F2%5Ca

n%5B1%5D+=+%28-%281%29%2Bsqrt%28+37+%29%29%2F2%5C1+=+2.54138126514911

n%5B2%5D+=+%28-%281%29-sqrt%28+37+%29%29%2F2%5C1+=+-3.54138126514911

Quadratic expression 1n%5E2%2B1n%2B-9

can be factored:
1n%5E2%2B1n%2B-9+=+1%28n-2.54138126514911%29%2A%28n--3.54138126514911%29

Again, the answer is: 2.54138126514911, -3.54138126514911. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-9+%29

The quadratic shows us that when n is equal to -3.54 or 2.54, the equation is equal to 10, which is a multiple of five.

Triangles/711694: If the legs of a 45-45-90 triangle have a length of 8 centimeters what is the perimeter of the triangle..?

1 solutions

Answer 437550 by Stitch(352) on 2013-02-07 11:42:06 (Show Source):

You can put this solution on YOUR website!
For this problem you could use the Pythagorean theorem.
The Pythagorean theorem states that for any right triangle A%5E2+%2B+B%5E2+=+C%5E2

Where A and B are the sides of the triangle and C is the hypotenuse.
----------------------
Use the theorem to solve for C
A = 8
B = 8
A%5E2+%2B+B%5E2+=+C%5E2

Take the squar root of both sides
sqrt%28128%29+=+C

*Note that value is rounded.
-------------------------
Now add all of the sides together to find the perimeter.
8+%2B+8+%2B+11.31+=+27.31

The perimeter is 21.31cm

Expressions-with-variables/709235: The sum of two numbers is thirty.using x to repersent the smaller of the two numbers, translate " the difference between six more thn the large number and twice the smallest number "into a variable expression in x. Then Simplify.
1 solutions

Answer 436471 by Stitch(352) on 2013-02-01 11:48:47 (Show Source):

You can put this solution on YOUR website!
x = small number
(30 - x) = large number
I think this is what you are asking for:
%28%2830+-+x%29+%2B+6%29+-+2x

Simplify

Combine like terms
36+-+3x

-----------------
You can stop ther or you could factor out a 3
3%2A%2812+-+x%29

Numbers_Word_Problems/709248: The sum of three consecutive odd numbers is 69. What is the smallest of these numbers?
1 solutions

Answer 436468 by Stitch(352) on 2013-02-01 11:36:45 (Show Source):

You can put this solution on YOUR website!
Equation 1: B+=+A+%2B+2

Equation 2: C+=+A+%2B+4

Equation 3: A+%2B+B+%2B+C+=+69

-----------------------------------
Note that B & C are written in terms of A. Substitute their values into equation 3.
Equation 3: A+%2B+B+%2B+C+=+69

A+%2B+%28A+%2B+2%29+%2B+%28A+%2B+4%29+=+69

Combine like terms
3A+%2B+6+=+69

Subtract 6 from both sides
3A+=+63

Divide both sides by 3
highlight%28A+=+21%29

Now plug 21 into equations 1 & 2 for A.
-----------------------------------
Equation 1: B+=+A+%2B+2

-----------------------------------
Equation 2: C+=+A+%2B+4

The smallest number is 21.

test/709237: pete is 6 years older than nick. nick is 7 years younger than howie. if pete is 19 years old,how old is howie?
1 solutions

Answer 436466 by Stitch(352) on 2013-02-01 11:31:16 (Show Source):

You can put this solution on YOUR website!
Let P = Pete's age.
Let N = Nick's age.
Let H = Howie's age.
---------------------
Given: P = 19.
N+=+P+-+6

---------------------
H+=+7+%2B+N

Howie is 20.

Numbers_Word_Problems/709239: A number of two digits is increased by 45 when the digits are reversed. The sum of the two digits is 9. find the number
1 solutions

Answer 436465 by Stitch(352) on 2013-02-01 11:26:20 (Show Source):

You can put this solution on YOUR website!
The Setup
Equation 1: A+%2B+B+=+9

(The sum of the digits is 9)
Equation 2: 10A+%2B+B+%2B+45+=+A+%2B+10B

(The number is increased by 45 when the digits are reversed)
------------------------
Solution
Solve equation 1 for one of the variables. I will solve for A.
Equation 1: A+%2B+B+=+9

Now plug (9-B) into equation 2 for A.
Equation 2: 10A+%2B+B+%2B+45+=+A+%2B+10B

10%289-B%29+%2B+B+%2B+45+=+%289-B%29+%2B+10B

Multiply the 10 through.
90+-+10B+%2B+B+%2B+45+=+9+-+B+%2B+10B

Combine like terms.
135+-+9B+=+9+%2B+9B

Add 9B to both sides.
135+=+9+%2B+18B

Subtract 9 from both sides.
126+=+18B

Divide both sides by 18.
highlight%287+=+B%29

Now solve for A, while using 7 for B.
A+=+9+-+B

{From earlier in the problem)
A+=+9+-+%287%29

The number was 27.

Travel_Word_Problems/709242: At 1:00 pm my elevation was 5620 feet above sea level. By 2:30 pm I had reached an elevation of 6040 feet above sea level.
What is the constant rate that I am climbing at?
1 solutions

Answer 436463 by Stitch(352) on 2013-02-01 11:12:07 (Show Source):

You can put this solution on YOUR website!
The constant climbing rate is the cahnge in distance divide by the cahnge in time.
The change in time from 1:00pm to 2:30pm is 1.5 hours.
Let climbing rate = R
R+=+%286040+-+5620%29%2F%281.5%29

R = 280ft per hour
You can also divide that number by 60 to convert it to feet per minute.

Evaluation_Word_Problems/708804: A barrel contains 150 gallons of paint and the is being drained at a constant rate of 10 gallon per hour. write an equation that model the number of gallons,g,after t hours
1 solutions

Answer 436257 by Stitch(352) on 2013-01-31 11:55:06 (Show Source):

You can put this solution on YOUR website!
g+=+150+-+10t

Note that t is greater than or equal to zero (Since time is positive)
but less than or equal to 15. (since you can not have a negative amount of paint)

Rate-of-work-word-problems/708802: Jack typed 80 words per minute when he enrolled in a typing course. His typing speed increased by 3% two weeks into the course. At the end of the course, Jack was able to type his entire 1680 word document in 20 minutes.
What was the percent of increase in his typing speed from the beginning of the course to the end.
A. 3%
B. 4%
C. 5%
D. 6%
E. 7%
I chose 5 % as 1680/20 means his new typing speed is 84. Therefore the percentage increase in writing speed is (84-80)/80 = 0.05 which means a percentage increase of 5. Is this the correct answer? Thanks for your assistance.
1 solutions

Answer 436256 by Stitch(352) on 2013-01-31 11:50:14 (Show Source):

You can put this solution on YOUR website!
Yes, 5% is the correct answer. And you solved it the right way. Nice job.

Age_Word_Problems/708800: at the present time a man is four times as old as his son six years ago he was 10 times as old.
1 solutions

Answer 436255 by Stitch(352) on 2013-01-31 11:42:58 (Show Source):

You can put this solution on YOUR website!
Let A = th eage of the dad
Let B = the age of the son
Equation 1: A+=+4B

Equation 2: A+-+6+=+10%2A%28B-6%29

-----------------------------
Since equation 1 is solved for A, plug 4B into equation 2 for A
Equation 2: A+-+6+=+10%2A%28B-6%29

Multiply the 10 through
4B+-+6+=+10B+-+60

Subtract 4B from both sides
-6+=+6B+-+60

Add 60 to both sides
54+=+6B

Divide both sides by 6
highlight%289+=+B%29

Now plug 9 into equation 1 for B
Equation 1: A+=+4B

______________________________________________________________________
______________________________________________________________________
Extra question #1:
The line y=mx+c passes through (2'5) and (4'13). Find the m and the c.
In that equation m is the slope and c is the Y-intercept.
Points on a graph are given in the form (X,Y).
The equation to find the slope of the line between to points is:
m+=+%28Y2-Y1%29%2F%28X2-X1%29

Now we will plug in the values you were given to solve for m.
m+=+%2813-5%29%2F%284-2%29

Since we know what m equals, we can rewrite the equation of the line.
y = mx+c is now y = 4x+c
The next step is to pick one of the points that you were gven and solve for c.
I will you the point (2,5)
That means that when x=2, then y=5
Plug those values into the line equation
y+=+4x+%2B+c

Subtract 8 from both sides
highlight%28-3+=+c%29

The equation of the line that passes through the given points is y = 4x - 3
______________________________________________________________________
______________________________________________________________________
Extra question #2:
Twice one Number added to 3 times a nother gives 21. Find the numbers if the difference between them is 3.
-------------------
Equation 1: 2A+%2B+3B+=+21

Equation 2: A+=+B+%2B+3

Since equation 2 is solved for A, plug (B + 3) into equation 1 for A.
Equation 1: 2A+%2B+3B+=+21

Multiply the 2 through
2B+%2B+6+%2B+3B+=+21

Combine like terms
5B+%2B+6+=+21

Subtract 6 from both sides
5B+=+15

Divide both sides by 5
highlight%28B+=+3%29

Now plug 3 into equation 2 for B.
Equation 2: A+=+B+%2B+3

Linear-equations/708795: In12 years a man will be twice as old as he was 12 years ago. Find his present age.

1 solutions

Answer 436253 by Stitch(352) on 2013-01-31 11:35:55 (Show Source):

You can put this solution on YOUR website!
Let A = the present age of the man.
2%2A%28A+-+12%29+=+A+%2B+12

Multiply the 2 through
2A+-+24+=+A+%2B+12

Add 24 to both sides
2A+=+A+%2B+36

Subtract A from both sides
highlight%28A+=+36%29

The man is currently 36.
12 years ago he was 24.
In 12 years he will be 48.
24 x 2 = 48

Linear_Equations_And_Systems_Word_Problems/707704: Admission to an amusement park is 8 dollars for adults and 5 dollars for children.if 201 was paid for 33 tickets, how many of each were purchased
1 solutions

Answer 435825 by Stitch(352) on 2013-01-29 11:48:26 (Show Source):

You can put this solution on YOUR website!
Let A = number of adult tickets
Let C = number of child tickets
Equation 1: 8A+%2B+5C+=+201

Equation 2: A+%2B+C+=+33

--------------------------------
Solve equation 2 for one of the variables.
Equation 2: A+%2B+C+=+33

Plug (33-C) into equation 1 for A
Equation 1: 8A+%2B+5C+=+201

Multiply the 8 through.
264+-+8C+%2B+5C+=+201

Combine like terms.
264+-+3C+=+201

Subtract 264 from both sides.
-3C+=+-63

Divide both sides by -3.
highlight%28C+=+21%29

Now solve for A, using 21 for C
A+=+33+-+C

Age_Word_Problems/707703: Maria's age is 15 year less than orldando's age. The sum of their ages is 29 what their ages?
1 solutions

Answer 435821 by Stitch(352) on 2013-01-29 11:39:26 (Show Source):

You can put this solution on YOUR website!
Let M = Maria's age
Let R = Orlando's age
Equation 1: M+=+R+-+15

Equation 2: M+%2B+R+=+29

-----------------------------
Note that equation one is solved for M.
Plug (R - 15) into equation 2 for M
Equation 2: M+%2B+R+=+29

Combine like terms
2R+-+15+=+29

Add 15 to both sides.
2R+=+44

Divide both sides by 2.
highlight%28R+=+22%29

Now plug 22 into equation 1 for R
Equation 1: M+=+R+-+15

Numbers_Word_Problems/707688: One positive number is 10 times another number. The difference between the two numbers is 81, find the numbers.
1 solutions

Answer 435819 by Stitch(352) on 2013-01-29 11:34:26 (Show Source):

You can put this solution on YOUR website!
Equation 1: A+=+10B

Equation 2: A+-+B+=+81

-----------------------------
Since equation 1 is already solved for A, plug 10B into equation 2 for A
Equation 2: A+-+B+=+81

Combine like terms
9B+=+81

Divide both sides by 9
highlight%28B+=+9%29

Now plug 9 into equation 1 for B
Equation 1: A+=+10B

test/707696: The sum of a numberand twice a second number is 14. when the second number is subtracted from the first number, the difference is 2.find the two numbers
1 solutions

Answer 435818 by Stitch(352) on 2013-01-29 11:26:43 (Show Source):

You can put this solution on YOUR website!
Equation 1: A+%2B+2B+=+14

Equation 2: A+-+B+=+2

------------------------------
Solve one of the equations for one of the variables.
Equation 2: A+-+B+=+2

Now plug (2 + B) into equation 1 for A
Equation 1: A+%2B+2B+=+14

Combine like terms
2+%2B+3B+=+14

Subtract 2 from both sides
3B+=+12

Divide both sides by 3
highlight%28B+=+4%29

Now solve for A, using 4 for B.
A+=+2+%2B+B

Inequalities/707695: -x when x = -54
1 solutions

Answer 435817 by Stitch(352) on 2013-01-29 11:22:32 (Show Source):

You can put this solution on YOUR website!
If x = -54.
Then -x equals 54.

Problems-with-consecutive-odd-even-integers/707693: find three consecutive even integers such that the sum of the smallest and 3 times the second is 38 more than twice the third.
1 solutions

Answer 435816 by Stitch(352) on 2013-01-29 11:19:58 (Show Source):

You can put this solution on YOUR website!
Equation 1: B+=+A+%2B+2

Equation 2: C+=+A+%2B+4

Equation 3: A+%2B+3B+=+2C+%2B+38

-----------------------------------
Note that B & C are written in terms of A. Substitute their values into equation 3.
Equation 3: A+%2B+3B+=+2C+%2B+38

A+%2B+3%2A%28A+%2B+2%29+=+2%2A%28A+%2B+4%29+%2B+38

Multiply through
A+%2B+3A+%2B+6+=+2A+%2B+8+%2B+38

Combine like terms
4A+%2B+6+=+2A+%2B+46

Subtract 6 from both sides
4A+=+2A+%2B+40

Subtract 2A from both sides
2A+=+40

Divide both sides by 2
highlight%28A+=+20%29

Now plug 20 into equations 1 & 2 for A.
-----------------------------------
Equation 1: B+=+A+%2B+2

-----------------------------------
Equation 2: C+=+A+%2B+4

Linear-equations/707098: PLEASE HELP ME TO SOLVE THIS PROBLEM (IF THE SUM OF TWO NUMBERS IS 84 AND YHEIR DIFFERENCE IS 30 FIND THOSE TWO NUMBERS?)

1 solutions

Answer 435542 by Stitch(352) on 2013-01-28 12:00:55 (Show Source):

You can put this solution on YOUR website!
Equation 1: A+%2B+B+=+84

Equation 2: A+-+B+=+30

Solve equation 2 for A
A+=+B+%2B+30

Now plug (B + 30) into equation 1 for A
Equation 1: A+%2B+B+=+84

Combine like terms
2B+%2B+30+=+84

Subtract 30 from both sides
2B+=+54

Divide both sides by 2
highlight%28B+=+27%29

Now plug 27 into equation 2 for B
A+=+B+%2B+30

Angles/707133: two angles of a triangle is the same size. the third angle is 12 degrees smaller than the first angle. find the measure the angle

1 solutions

Answer 435540 by Stitch(352) on 2013-01-28 11:56:04 (Show Source):

You can put this solution on YOUR website!
The sum of the angles of a triangle equal 180
Equation 1: A+%2B+B+%2B+C+=+180

Equation 2: A+=+B

Equation 3: A+-+12+=+C

------------------------------
Note that equations 2 and 3 are written in terms of A. You can substitute the values of B & C into equation 1.
Equation 1: A+%2B+B+%2B+C+=+180

Combine like terms
3A+-+12+=+180

Add 12 to both sides
3A+=+192

Divide both sides by 3
highlight%28A+=+64%29

------------------------------
Now plug 64 into equation 2 for A
Equation 2: A+=+B

------------------------------
Now plug 64 into equation 3 for A
Equation 3: A+-+12+=+C

Polynomials-and-rational-expressions/707140: Am trying to help my God daughter: She's having issues with a problem that I do not understand or remember. Hope you can help with steps such as what is the q mean, know some algebra but the factoring is what's stumping me.
Thank you.
15q^3 power + 40q^2 power + 3q + 8 .
1 solutions

Answer 435538 by Stitch(352) on 2013-01-28 11:47:26 (Show Source):

You can put this solution on YOUR website!
Given: 15q%5E3+%2B+40q%5E2+%2B+3q+%2B+8

In that equation the q is just a variable. It can be replaced by any other letter and still mean the same thing.
--------------------------------------------
You did not mention what you were solving for so I will just factored the equation.
For an equation that goes to the third power, it is usually easier (in my opinion) to group the equation and find the greatest common factor.
For example, group the first two terms and then group the second two terms.
%2815q%5E3+%2B+40q%5E2%29+%2B+%283q+%2B+8%29

%2815q%5E3+%2B+40q%5E2%29+%2B+%283q+%2B+8%29

The greatest common factor of the first two terms is 5q^2
The second two terms do not have a common factor and will stay as is.
Rewrite the equation.
5q%5E2%2A%283q+%2B+8%29+%2B+%283q+%2B+8%29

5q%5E2%2A%283q+%2B+8%29+%2B+%283q+%2B+8%29

Notice that both parts now contain a (3q + 8). You can factor that out and rewrite the equation.
%283q+%2B+8%29%2A%285q%5E2+%2B+1%29

I hope that helps.

Quadratic_Equations/707142: 216 is 60% of?

1 solutions

Answer 435537 by Stitch(352) on 2013-01-28 11:29:50 (Show Source):

You can put this solution on YOUR website!
To change a percent to a decimal, divide the percent by 100
60% / 100 = 0.6
X+%2A+0.6+=+216

Divide both sides by 0.6
highlight%28X+=+360%29

Angles/707143: angles a and angle b are supplementary angles find the measure of each angle if angle a is 30 greater than angle b
1 solutions

Answer 435536 by Stitch(352) on 2013-01-28 11:26:52 (Show Source):

You can put this solution on YOUR website!
Two angles are supplements when they add up to 180
Equation 1: A+%2B+B+=+180

Equation 2: A+=+B+%2B+30

-----------------------------
Plug (B + 30) into equation 1 for A
Equation 1: A+%2B+B+=+180

Combine like terms
2B+%2B+30+=+180

Subtract 30 from both sides
2B+=+150

Divide both sides by 2
highlight%28B+=+75%29

Now plug 75 into equation 2 for B
Equation 2: A+=+B+%2B+30

Graphs/705748: I am trying to graph this line y+4/5x-10
I know th y intercept is (0,-10) I am having a hard time coming up with the x intercept what I came up with is (0,10.3)
x=-10-4/5
x=54/5
x=10.3
1 solutions

Answer 434779 by Stitch(352) on 2013-01-24 11:54:37 (Show Source):

You can put this solution on YOUR website!
I think you meant to type Y = 4/5X - 10
--------------------
The standard eqaution of a line is Y = mX = b
Where m is the slope and b is the Y-intercept.
So yes, (0,-10) is the Y-intercept.
--------------------
The X intercept is found when Y is equal to zero.
0+=+%284%2F5%29X+-+10

Add 10 to both sides
10+=+%284%2F5%29X

Multiply both sides by 5/4
%285%2F4%29%2A10+=+cross%28%285%2F4%29%2A%284%2F5%29%29%2AX

Simplify

The x-intercept is (12.5,0)
graph%28300%2C300%2C-20%2C20%2C-20%2C20%2C%284%2F5%29x-10%29

Travel_Word_Problems/705762: in a football game, the quaterback is 15 yards away from making a first down and is running at 264 years per minute. after 0.03 of a minute, a linebacker who is 15 yards on the opposite side of the down marker begins running directly towards the quaterback at 440 yards per minute. will the linebacker be able to tackle the quaterback before he gets the first down ?
1 solutions

Answer 434778 by Stitch(352) on 2013-01-24 11:42:24 (Show Source):

You can put this solution on YOUR website!
The quaterback:
%2815cross%28yards%29%2F1%29%2A%281minute%2F264cross%28yards%29%29+=+0.0568minutes

-----------------------------------------
The Linebacker:

Going by the numbers, no the linebacker will not be able to tackle the quarterback in time.
**But in reality these numbers are only fractions of a second different.

Rectangles/705761: Find the dimentions of a rectangle whose lenth is one foot longer than twice its width and whose perameter is 20 feet.
1 solutions

Answer 434774 by Stitch(352) on 2013-01-24 11:25:44 (Show Source):

You can put this solution on YOUR website!
Set-Up:
Equation 1: L+=+2W+%2B+1

Equation 2: P+=+2L+%2B+2W

(The perimeter of a rectangle
P = 20
-----------------------------
Since equation 1 is already solved for L, plug (2W + 1) into equation 2 for L
Equation 2: P+=+2L+%2B+2W

Multiply the 2 through
20+=+4W+%2B+2+%2B+2W

Combine like terms
20+=+6W+%2B+2

Subtract 2 from both sides
18+=+6W

Divide both sides by 6
highlight%283+=+W%29

Now plug 3 into equation 1 for W
Equation 1: L+=+2W+%2B+1

Miscellaneous_Word_Problems/705759: There is a 3 degree drop in tempature for every 1'000 feet that an airplane climbs in the sky. If the tempature on the ground is 50 degrees, what will be the tempature when the plane reaches an altitude of 24,000 feet?
1 solutions

Answer 434773 by Stitch(352) on 2013-01-24 11:20:25 (Show Source):

You can put this solution on YOUR website!
24,000ft / 1000ft = 24
24 * 3 degrees = 72
50 degrees - 72 degrees = -22 degrees
At 24,000 the temperature is -22 degrees

Age_Word_Problems/705325: you were 4 years old,your sister was 3 times your age,now that your are 12 years old,how old is your sister
1 solutions

Answer 434519 by Stitch(352) on 2013-01-23 15:01:52 (Show Source):

You can put this solution on YOUR website!
When you were 4, your sister was three times your age.
4*3 = 12
When you were 4 your sister was 12.
Now you are 12.
12-4 = 8
Add 8 to your sister's past age
12 + 8 = 20
Now that you are 12, your sister is 20

Mixture_Word_Problems/705286: Dave is 4 years older than Billy. Billy is 3 times older than Jon. All three of their ages combined is 39. What is the age of each child?
I started the problem by trying to figure out Jon's age. I came up with the answer of 7. That does not add up correctly. It looks the answer should be 5. I need the steps to get to 5. Trying to help my son with this problem last night and I am stumped.
Thanks
1 solutions

Answer 434494 by Stitch(352) on 2013-01-23 11:58:27 (Show Source):

You can put this solution on YOUR website!
Let B = Billy's Age
Let D = Dave's Age
Let J = Jon's Age
Equation 1: D+=+B+%2B+4

Equation 2: B+=+3J

Equation 3: B+%2B+D+%2B+J+=+39

--------------------------------
Rewrite equation 2 so that it is solved for J
B%2F3+=+J

Now both equation 1 and equation 2 are in terms of B
Substitue those values into equation 3 for the same letter.
Equation 3: B+%2B+D+%2B+J+=+39

B+%2B+%28B+%2B+4%29+%2B+%28B%2F3%29+=+39

Multiply everything by 3 to remove the denominator
3B+%2B+3B+%2B+12+%2B+B+=+117

Combine like terms
7B+%2B+12+=+117

Subtract 12 from both sides
7B+=+105

Divide both sides by 7
highlight%28B+=+15%29

Now plug 15 into the equations 1 and 2 for B.
---------------------------------------------
Equation 1: D+=+B+%2B+4

---------------------------------------------
B%2F3+=+J

Equations/705278: I need to solve for x and show work --> (2/x-2)=(4/x-3)-(1/x+1)
1 solutions

Answer 434491 by Stitch(352) on 2013-01-23 11:42:42 (Show Source):

You can put this solution on YOUR website!
Given:: 2%2F%28X-1%29+=+4%2F%28X-3%29+-+1%2F%28X%2B1%29

I would start by multiplying everything by each of the denominators

Then the denominators will cancel out

Rewrite the equation.
2%2A%28X-3%29%2A%28X%2B1%29+=+4%2A%28X-1%29%2A%28X%2B1%29+-+1%2A%28X-1%29%2A%28X-3%29

Start to multiply through
%282X+-+6%29%2A%28X%2B1%29+=+%284X-4%29%2A%28X%2B1%29+%2B+%28-X%2B1%29%2A%28X-3%29

Multiply through
2X%5E2+%2B+2X+-+6X+-+6+=+4X%5E2+%2B+4X+-+4X+-+4+-+X%5E2+%2B+3X+%2B+X+-+3

Combine like terms
2X%5E2+-+4X+-+6+=+3X%5E2+%2B+4X+-+7

Subtract 2X^2 from both sides
-4X+-+6+=+X%5E2+%2B+4X+-+7

Add 4X to both sides
-6+=+X%5E2+%2B+8X+-+7

Add 6 to both sides
0+=+X%5E2+%2B+8X+-+1

Now use the quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation aX%5E2%2BbX%2Bc=0

(in our case 1X%5E2%2B8X%2B-1+=+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

.

Discriminant d=68 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+68+%29%29%2F2%5Ca

X%5B1%5D+=+%28-%288%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+0.123105625617661

X%5B2%5D+=+%28-%288%29-sqrt%28+68+%29%29%2F2%5C1+=+-8.12310562561766

Quadratic expression 1X%5E2%2B8X%2B-1

can be factored:
1X%5E2%2B8X%2B-1+=+1%28X-0.123105625617661%29%2A%28X--8.12310562561766%29

Again, the answer is: 0.123105625617661, -8.12310562561766. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-1+%29

So X = 0.1231 & -8.1231

Expressions-with-variables/705284: 3. Determine which value makes the open sentence true.
12 + 3x = 30
(Points : 1)
x = 2
x = 4
x = 5
x = 6

1 solutions

Answer 434490 by Stitch(352) on 2013-01-23 11:21:56 (Show Source):

You can put this solution on YOUR website!
Given: 12+%2B+3X+=+30

Subtract 12 from both sides
3X+=+18

Divide both sides by 3
highlight%28X+=+6%29

See tutors' answers!

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