Question 421710: I am not sure if this is the area to do this question in but here goes. I am doing a practice final, and this question has me stumped.
The owner of a rectangular swimming pool, with dimensions 10 meters by 25 meters, wants to surround the pool with a concrete border of uniform width. The owner has enough concrete mix to cover 74 square meters. How wide should the border be?
I need the equation from beginning to end. So far I have
(2l+25)(2w+10)-250=74
(50l)(20w)
My original answer was 4 meters wide but that's wrong, I already know that the answer needs to be 2 meters wide but I can't figure out the equation to get me to the correct answer.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! he owner of a rectangular swimming pool, with dimensions 10 meters by 25 meters, wants to surround the pool with a concrete border of uniform width. The owner has enough concrete mix to cover 74 square meters. How wide should the border be?
:
Let x = the width of the concrete border
:
The the overall dimensions will be (2x+10) by (2x+25)
:
overall area - pool area = 74 sq/m
(2x+10)(2x+25) - 250 = 74; (which essentially, is what you have)
FOIL
(4x^2 + 50x + 20x + 250) - 250 = 74
4x^2 + 70x - 74 = 0
Simplify, divide by 2
2x^2 + 35x - 37 = 0
Factors to
(2x + 37)(x - 1) = 0
Positive solution
x = 1 meter wide
:
:
You said it should be 2, check this by finding the overall area, subtract this pool area:
(2(1) + 10)(2(1) + 25) - 250 =
(2+10)(2+25) - 250 =
(12 * 27) - 250
324 - 250 = 74, confirms our answer of x = 1
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