# Questions on Algebra: Equations answered by real tutors!

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Question 994710: - 3 + 5a = 4a - 10
Found 2 solutions by MathTherapy, Boreal:
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- 3 + 5a = 4a - 10

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-3 +5a=4a-10
a=13, by adding 3 to both sides and subtracting 4a from both sides
===
check
-3+65=52+10
62=62

Question 994653: sams science marks is 15 less than his maths mark.the total of his two marks is 145.find sams marks for each subject.
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sams science marks is 15 less than his maths mark.the total of his two marks is 145.find sams marks for each subject.
-----------
Equations:
s = m-15
s+m = 145
------
Substitute for "s" and solve for "m"::
m-15 + m = 145
2m = 160
m = 80 (his math mark)
s = 145-80 = 65 (his science mark)
---------
Cheers,
Stan H.
----------

Question 994495: What would be the tip amount for 83.95,if I left a 15% tip ?
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.
(0.15)($83.95)=$12.59

Question 994457: I don't know algebra. I need this question answered: What is the equation 5+3 = ?
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I don't know algebra. I need this question answered: What is the equation 5+3 = ?
----------------
That's not an equation because there's nothing on the right side.
-----
It's just arithmetic.

Question 994384: A total investment of $9,700is made into two savings accounts. One account yields 9% simple interest and the other 10% simple interest. He earns a total of$935.00interest for the year. How much was invested in the 9% account?
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x=amount in 9%
9700-x=amount at 10%
interest= .09x+(9700-x)(.10)=935
0.09 + 970-(.10x)=935 by distributing
-0.01x=-35. multiply by $100 x=3500 @9%=$315
$6200 @10%=$620
They sum to $935 Question 994373: elimination method for 5x-5y=-5; -5x+2y=-10 Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! +5x-5y=-5 -5x+2y=-10 -------------- Add Question 994285: The total profit$P, generated from the production and marketing of n items of a certain product is given by
P = −10800n − 4 n^3 + 600n^2 −122
How many items should be made for maximum profit? What is the maximum profit?
Enter your answers as a list [in square brackets] of the form: [ n, p]
for some number of items n and profit p
This is what I have
P = −10800n − 4 n^3 + 600n^2 −122
P' = -10800 -12n^2 + 1200n
-10800 -12n^2 + 1200n = 0
n = 10, n = 90
But I am not sure what to do from there?
Do I sub them in?
-10800 -12(10)^2 + 1200(10) = 0
-10800 -12(90)^2 + 1200(90) = 0
I'm lost!
Thank you!!

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The total profit $P, generated from the production and marketing of n items of a certain product is given by P = −10800n − 4 n^3 + 600n^2 −122 How many items should be made for maximum profit? What is the maximum profit? Enter your answers as a list [in square brackets] of the form: [ n, p] for some number of items n and profit p This is what I have P = −10800n − 4 n^3 + 600n^2 −122 P' = -10800 -12n^2 + 1200n -10800 -12n^2 + 1200n = 0 n = 10, n = 90 But I am not sure what to do from there? Do I sub them in? -10800 -12(10)^2 + 1200(10) = 0 -10800 -12(90)^2 + 1200(90) = 0 I'm lost! Thank you!! You're correct up to this point: -------> Now, maximum profit (P) is realized at: With b being 1200, and a being - 12, becomes: , or , or 50 Number of units at which maximum profit occurs is: As mentioned before, this means that maximum profit is realized at n = 50 (I presume this should be in 000s, or millions) units -------- Substituting 50 for n P, or maximum profit = - 30,000 + 60,000 - 10,800, or This results in: [n, P], or [] Question 994207: What is the solution to 5x+9=x-23 ? Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! What is the solution to 5x+9=x-23 ? ---- Subtract x from both sides: Subtract 9 from both sides: 4x = -32 ---- Divide both sides by 4 to get: x = -8 ----- Cheers, Stan H. --------- Question 994056: Find the difference quotient and simplify for the following function: f(x)=-10x^2 + 10x +8. Thanks for your help. Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! h, some small quantity which can be made as small as you wish be never being 0. Difference Quotient is , look at the terms in the numerator carefully.... You might then ask, "what happens as h approaches 0?" Question 994110: write an equation that has variables on both sides and has a solution of -3 Answer by ikleyn(988) (Show Source): You can put this solution on YOUR website! . 2x = x - 3. Question 994089: 1/2x+6=10 Answer by rfer(15570) (Show Source): You can put this solution on YOUR website! 1/2x=10-6 x=4/(1/2) x=4*2/1 x=8 Question 994087: The equation 3w^2+5w represents the area of a rectangle where w is width. What is the length in terms of w? Answer by rothauserc(2272) (Show Source): You can put this solution on YOUR website! length(l) * width(w) = area of rectangle we know the area of the rectangle is 3w^2+5w, then l * w = 3w^2+5w divide both sides of = by w l = 3w + 5 Question 994051: 14 is added to 2/3 of a certain number the results is 5/4 times the original number.find the number Answer by rfer(15570) (Show Source): You can put this solution on YOUR website! 2/3x+14=5/4x 14=5/4x-2/3x 14=15/12x-8/12x 14=7/12x 14/(7/12)=14 14*12/7=x 24=x Question 994035: The Booster Club has a goal of raising at least$300. The Club has already raised $75. The Booster Club is sponsoring a pancake breakfast and charging$5.00 per ticket.
What inequality would represent the number of tickets (t) that the Booster Club must sell to meet its goal?
I have seen this question and similar posted - providing the number of tickets that need to be sold does NOT provide a statment of inequality and THAT is the answer to the question - a statement of inequality. it should read something as follows (the variable t should be included) is equal to or greater than 300.

Found 2 solutions by MathTherapy, josgarithmetic:
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The Booster Club has a goal of raising at least $300. The Club has already raised$75. The Booster Club is sponsoring a pancake breakfast and charging $5.00 per ticket. What inequality would represent the number of tickets (t) that the Booster Club must sell to meet its goal? I have seen this question and similar posted - providing the number of tickets that need to be sold does NOT provide a statment of inequality and THAT is the answer to the question - a statement of inequality. it should read something as follows (the variable t should be included) is equal to or greater than 300. Proceeds from the sale of tickets (t), plus amount already raised, is greater than, or equal to total to be raised, OR Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! x, how many tickets needed; If the sales revenue is what is necessary and nothing about cost involved, then your aim is to make the 300-75=225 dollars yet to fill. Want at least 225 dollars, and each ticket bring in (if just revenue) 5 dollars. . Question 993997: 3x + 4 5x+6 _____ - ____ 2x 3x (3x+4 / 2x) - (5x+6 / 3x) Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! 3x + 4 5x+6 _____ - ____ 2x 3x ====================================== lcd = 6x ------------- (3x+4)/2x - (5x+6)/3x = (3)(3x+4) - (2)(5x+6)]/[6x] ------------- [9x+12-10x-12]/6x ------------- [-x/6x] = -(1/6) ===================================== Cheers, Stan H. -------- Question 993998: show that the quadratic equation x^2+2px＋p(p－1)＝0 has two unequal real roots for any positive values of p. Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! and p is given to be a real number . This means the square root expression does not disappear, and the plus&minus nature of the two roots insures that x is two unequal values. or Question 993902: A manufacturer has 2900 units in stock. The product is now selling at$8 per unit. Next month the unit price will increase by $0.50. The manufacturer wants the total revenue received from the sale of the 2900 units to be no less than$23750. What is the number of units that can be sold this month?
At most _______ units

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if he sold all 2900 at 8 dollars each, he would get 23200 total.

that's 550 short of his goal of at least 23750.

the difference in price between 8 and 8.50 is .50.

take the 550 and divide it by .50 and you get 1100.

he would need to sell a minimum of 1100 units at 8.50.

2900 - 1100 = 1800.

he would therefore sell 1800 at 8.00 and 1100 at 8.50 and he would get 8 * 1800 = 14,400 + 8.50 * 1100 = 9,350 for a total orf 23,750.

you can also solve this algebraically as follows:

x = number of units sold at 8 dollars each.
y = number of units sold at 8.5 dollars each.

first equation is x + y = 2900
second equation is 8x + 8.5y >= 23750

from the first equation, solve for y to get y = 2900 - x

replace y with 2900 - x in the second equation to get:

8x + 8.5 * (2900-x) >= 23750

simplify to get:

8x + 24650 - 8.5x >= 23750

subtract 8x from both sides of this equation and subtract 23750 from both sides of this equation to get:

24650 - 23750 = 8.5x - 8x

simplify to get:

900 = .5x

divide both sides of this equation by 1.5 to get:

x = 1800.

since x + y = 2900, this means that y = 1100.

solution is x = 1800 and y = 1100

x is the number sold at 8 dollars
y is the number sold at 8.5 dollars

same answer as before when we used logic.

Question 993956: x/2-y/5=1
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Do you have a question?

Question 993903: One positive number is one-fifth of another number. The difference between the two numbers is 136, find the numbers.
The two numbers in increasing order are _____ and _________

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Call the larger one x. Thus the smaller will be (1.5)x. Their difference is
x - (1/5)x = 136
(4/5)x = 136
x = 170
and then
(1/5)(170) = 34
In increasing order they are 34 and 170.

Question 993901: Your weekly paycheck is 25 percent less than your coworker's. Your two paychecks total 850. Find the amount of each paycheck.

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Call your coworker's pay x. Your pay is 25% less or .75x. Thus
x + .75x = 850
1.75x = 850
x = 850/1.75 = $485.71 .75x =$364.29

Question 993904: Two cyclists, 45 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 3 hours later, what is the speed (in mi/h) of the faster cyclist?
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The easy way: They cover 45 miles in 3 hours. Their combined speed must be 15 miles an hour. Thus the slower guy travels at 5 mph and the faster at 10 mph.
The harder way: If we call the rate of the slower rider R, the faster rider travels at 2R. Since they travel the same 3 hours, one guy travels 3R miles and the other travels 6R miles. Added together, they cover 45 miles, or
3R + 6R = 45
9R = 45
R = 5
2R = 10 miles per hour

Question 993907: A rectangular room is 1.8 times as long as it is wide, and its perimeter is 27 meters. Find the dimension of the room.

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Choosing L for length and W for width, the first statement reads
L = 1.8W
Then, for perimeter, we have
P = 2L + 2W = 27
We substitute and get
2(1.8W) + 2W = 27
3.6W + 2W = 27
5.6W = 27
W = 27/5.6 = 270/56 = 135/28
L = 1.8W = (9/5)W = (9/5)(135/28) = 243/28

Question 993939: If x + .07x = 71.75, what does x equal?
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x + .07x = 71.75
1.07x = 71.75
Divide by 1.07

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.
= .

Multiply both sides by (x-4).

You will get

2*(x-4) + 5 = x+1.

Simplify:

2x - 8 + 5 = x + 1.

x = 4.

But  x = 4  is prohibited,  because the original equation has  (x-4)  in the denominators.  It is prohibited to divide by zero.

Thus the equation has no solutions.

 The plot of

Question 993899: 4(3x-2)=16
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.
x = 2.

Please be polite next time and write what you want to get (at least :-) ).

Question 993870: What does 3z to the -2 power equal?
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What does 3z to the -2 power equal?
------
= probably

Question 993867: Solve:x-3y=0 & x+y=16

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x -3y = 0
x + y = 16
----------------- Subtract

Question 993749: Find point P(x,y) on line y=2x-1 so that its distance from point Q(4,3) is 2
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you can solve this graphically easy enough if you have good graphing software.
using one, i found that two points satisfy the requirements.
those points are (2,3) and (2.8,4.60)

what you are looking for on the graph is the intersection of the line y = 2x-1 with the intersection of the circle whose equation is (x-4)^2 + (y-3)^2 = 4.

without graphing software it's not quite as easy, but can be done.

you are still looking for the intersection of the graph of the equations shown above, but you have to do it algebraically.

you have 2 equations:

y = 2x - 1
(x-4)^2 + (y-3)^2 = 4

the equation of y = 2x - 1 is a straight line.

the equation of (x-4)^2 + (y-3)^2 = 4 is a circle whose center is (4,3) and whose radius is 2.

replace y in the second equation with the value of y from the first equation to get:

(x-4)^2 + (2x-1-3)^2 = 4

simplify to get:

(x-4)^2 + (2x-4)^2 = 4

simplify the equation to get:

x^2 - 8x + 16 + 4x^2 - 16x + 16 = 4

combine like terms to get:

5x^2 - 24x + 32 = 4

subtract 4 from both sides of the equation to get:

5x^2 - 24x + 28 = 0

use the quadratic formula to find the values of x that satisfy that equation.

you will find that the values of x = 2 and x = 2.8 satisfy both equations and are therefore intersections of both equations on the graph.

when x = 2, y = 2x-1 becomes y = 3.
when x = 2.8, y = 2x-1 becomes 4.6.

the points on the circle that are also on the line are therefore (2,3) and (2.8,4.6)

both these points should be 2 units away from the center of the circle because the line segments formed by each of these points and the center of the circle is a radius of the circle.

the distance between two points on the graph is given by the equation:

d = sqrt((x1-x2)^2 + (y1-y2)^2).

the distance between (2,3) and (4,3) is equal to sqrt((4-2)^2 + (3-3)^2) which is equal to sqrt(2^2) which is equal to sqrt(4) which is equal to 2.

the distance between (2.8,4.6) and (4,3) is equal to sqrt((4-2.8)^2 + (3-4.6)^2) which is equal to sqrt(1.2)^2 + (-1.6)^2) which is equal to sqrt(1.44 + 2.56) which is equal to sqrt(4) which is equal to 2.

either one of these points will satisfy the requirements of this problem.

the graph of the line and the circle are shown below:

Question 993782: Are y=-1/5x+1 & 2x+10y=3 parallel, perpendicular or neither? I tried to do it on paper but its not making sense
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2x+10y=3
10y=-2x+3
y=-2/10x+3
y=-1/5x+3
-------------
y=-1/5x+1
The slopes are the same so they are parallel

Question 993756: 12 - 4/5 (x + 15) =4
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Do you have a question?

Question 993723: Solve
-3X +12+ 7X = 8+ 5X +4 -X

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Hi there,
-3X +12+ 7X = 8+ 5X +4 -X
Collect all the X's on the left and
the numbers on the right.
Remember if you change the side with an X or
a number you change the sign
-3X + 7X - 5X + X = 8 + 4 - 12
0 = 0
Hope this helps :-)

Question 993720: Hi! I really need some help with this problem I've been stuck on.
The length of a rectangle is 8 in. more than its width. The perimeter is 52 in.

What is the length of the rectangle?

Found 2 solutions by Cromlix, solver91311:
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Hi there,
Make the width = 'x'
Length = 8 + x
Perimeter = 2 x Width + 2 x Length
52 = 2(x) + 2(8 + x)
52 = 2x + 16 + 2x
Collect like terms.
2x + 2x = 52 - 16
4x = 36
x = 9
Width = 9 ins
Length = 17 ins.
Hope this helps :-)

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The length is 8 more than the width, so , then since the perimeter is ,

Solve for

John

My calculator said it, I believe it, that settles it

Question 993716: If x= 20 cm, calculate the area include units

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Seriously?

John

My calculator said it, I believe it, that settles it

Question 993195: 5-7+2x10=

Can you explain why ?
I need to know how this algebra expression is simplified .

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5 - 7 + 2 * 10 --> (-2) + (20) = 18

Do you see how I got the answer of 18?

Question 993500: Supposef(x)=3x–4and g(x)=|x|+3.
1) f(1/3) + g(-2)
2) f(1)/g(1)
I need the work on how to do this

Found 2 solutions by solver91311, MathLover1:
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1) Write the pattern for f(x) in pencil. Erase the x. Write (1/3) in the place where the x was. Do the indicated arithmetic. Do the same thing with g(x), substituting -2 in place of the x. Do the arithmetic. Sum your two results.

John

My calculator said it, I believe it, that settles it

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Suppose and .
1)
...(recall as as well)
2)

Question 993484: 2(2)^2-3(2)(-3)-2(-3)^2=

Question 993440: The length is 12 units more than then the width. perimeter is 7 times the width. find the length and width
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So

So

Solve for then calculate

John

My calculator said it, I believe it, that settles it

Question 993441: The length is 4 units less than 3 times the width. The perimeter is 22 units more than twice the width. Find the length and width
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Hint: If the perimeter of a rectangle is units greater than twice the width, then is equal to twice the length.

John

My calculator said it, I believe it, that settles it

1/x+1/(x-1)=2/(x^2-2x)

Found 2 solutions by MathTherapy, addingup:
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1/x+1/(x-1)=2/(x^2-2x)
, with:
------- Factoring out right-side denominator
(x - 1)(x - 2) + x(x - 2) = 2(x - 1) ------- Multiplying by LCD, x(x - 1)(x - 2)

As this trinomial CANNOT be factored, use the quadratic equation formula, or "completing the square" method to solve for x
You should get:
It would've been nice if you'd shown your "struggles!"

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You don't say by what method, it can be solved completing the squares or using the quadratic formula. Here is completing the squares:
Solve for x:
1/x+1/(x-1)=2/(x^2-2x) Rewrite for convenience: 1/(x-1)+1/x= 2/(x^2-2x)
Look for a polynomial to multiply both sides in order to get rid of fractions,
multiply by (x-1) (x^2-2x):
(x-2)(x-1)-2x+x^2 = 2(x-1)
Expand out terms of the left hand side:
2x^2-5x+2= 2(x-1)
Expand out the right hand side:
2 x^2-5 x+2 = 2 x-2
Subtract 2x-2 from both sides:
2x^2-7x+4 = 0
Divide both sides by 2 to simplify:
x^2-(7 x)/2+2= 0
Solve the quadratic equation by completing the square.
Subtract 2 from both sides:
x^2-(7x)/2 = -2
Take one half of the coefficient of x and square it, then add it to both sides.
x^2-(7x)/2+49/16= 17/16
Factor the left hand side.
(x-7/4)^2 = 17/16
Now eliminate the exponent on the left hand side by taking th sq rt both sides:
x-7/4= sqrt(17)/4 or x-7/4= -sqrt(17)/4
Now solve each equation separately:
x-7/4= sqrt(17)/4
x = 7/4+√(17)/4 or x-7/4 = -√(17)/4
Look at the second equation: Solve for x.