SOLUTION: 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 su

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

RELATED QUESTIONS
sasha works at the botanical gardens and is planning a new rectangular rose garden 20m by (answered by ankor@dixie-net.com)

Hi I need if anyone could help me with this prob.. 1. A carpet is to cover 2/3 of... (answered by ankor@dixie-net.com)

A rectangular pool has dimensions of 40 ft. and 60 ft. If the pool has a patio around it (answered by mananth)

A rectangular pool has dimensions of 40 ft. and 60 ft. If the pool has a patio around it... (answered by Earlsdon)

A rectangular tract of land 20m by 30m has part of its area covered by an I-shaped road,... (answered by ankor@dixie-net.com)

A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around... (answered by ankor@dixie-net.com)

A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around... (answered by checkley77)

You just had a pool installed that has dimensions 10 feet by 24 feet by 4 feet. You want... (answered by josgarithmetic,ikleyn)

You just had a pool installed that has dimensions 10 feet by 24 feet by 4 feet. You want... (answered by jorel1380,ankor@dixie-net.com,MathTherapy)