SOLUTION: A concrete mixer needs to know how wide to make a walk around a rectangular fountain that is 10 by 15 feet. She has enough concrete to cover 200 sq. ft. To the nearest tenth of a f
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Question 1183855: A concrete mixer needs to know how wide to make a walk around a rectangular fountain that is 10 by 15 feet. She has enough concrete to cover 200 sq. ft. To the nearest tenth of a foot, how wide should the walk be in order to use up all the concrete? Answer by ikleyn(52754) (Show Source):
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A concrete mixer needs to know how wide to make a walk around a rectangular fountain that is 10 by 15 feet.
She has enough concrete to cover 200 sq. ft. To the nearest tenth of a foot, how wide should the walk be in order to use up all the concrete?
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Let x be the uniform width of the concrete walk.
The outer dimensions of the concrete walk are (10+2x) and (15+2x) feet.
The area equation is
(10+2x)*(15+2x) - 10*15 = 200.
Simplify and reduce to the standard quadratic equation
4x^2 + 50x - 200 = 0,
or
2x^2 + 25x - 100 = 0.
It is not factorable, so apply the quadratic formula.
= = .
Take the positive root
x = = 3.2 (rounded).
ANSWER. The uniform width of the concrete walk is 3.2 feet.
