Question 729606: Hi I need help on this question
Sasha is planning to put a patio around her new pool which has dimensions of 20m by 30m. she wants the patio to have a uniform width,x,and to surround the entire pool. Her budget is $6000 and she knows it will cost $10/m^2 to construct the patio. How wide can she afford for the patio to be?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Sasha is planning to put a patio around her new pool which has dimensions of 20m by 30m. she wants the patio to have a uniform width,x,and to surround the entire pool. Her budget is $6000 and she knows it will cost $10/m^2 to construct the patio. How wide can she afford for the patio to be?
.
Let x = width of patio
then
area of "pool and patio" is:
(2x+20)(2x+30)
4x^2+60x+40x+600
.
our equation:
10((2x+20)(2x+30)- (20)(30))= 6000
10(4x^2+60x+40x+600 - 600)= 6000
10(4x^2+100x)= 6000
(4x^2+100x)= 600
4x^2+100x-600 = 0
x^2+25x-150 = 0
x^2+25x-150 = 0
(x+30)(x-5) = 0
x = {-30, 5}
throw out the negative solution (extraneous) leaving
x = 5 m
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