Question 1068410: Please help me with this question...
Marge has a flyer that is 10 inches wide and 12 inches long. To increase the size of the flyer, she will increase the length and width of the flyer by the same percent.
a. Write an equation that gives the new area A of the flyer in terms of x, where x is the percent increase in the length of the original flyer written as a decimal.
b. The area of the new flyer 270 square inches. Use your equation from part a to find the percent increase of the length of the flyer.
c. Explain an alternate way of finding the percent increase of the length of the flyer, without using the equation from part a.
Thank you in advance!
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! (10+x*10)(12+12*x) = 270
Expand using distributive properties of multiplication (10*12+10*12x etc.) and you'll get:
120+120x+120x+120x^2 = 270
120+240x+120x^2 = 270
120+240x+120x^2-270 = 0
240x+120x^2-150 = 0
rewrite:
120x^2+240x-150 = 0
120x^2+240x = 150
divide both sides by 120 and you get:
x^2+2x = 150/120 = 5/4
Now it gets tricky, I'm using the method of completing the squares:
The coefficient of x is 2. 2/2 = 1 Add the square of 1 to both sides of the equation:
x^2+2x+1^2 = 5/4+1^2
1^2 = 1, so rewrite:
x^2+2x+1 = 5/4+1
x^2+2x+1 = 9/4
factor x^2+2x+1:
(x+1)^2 = 9/4
Take the square root on both sides and we have 2 possible solutions:
x+1 = 3/2 or x+1 = -3/2
x = 3/2-2/2 = 1/2 or x = -3/2-2/2 = -5/2
We are not looking for a negative number, let's try 1/2 = 0.5 = 50%
Check:
10+(10*0.5)(12+(12*0.5) = 15*18 = 270 Correct.
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