SOLUTION: I need help solving this word problem. A club swimming pool is 30 feet wide and 40 feet long. The club members want an exposed aggregate border in a strip of uniform width around t

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Question 1171110: I need help solving this word problem. A club swimming pool is 30 feet wide and 40 feet long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 296 square feet. How wide can the strip be?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
u, the uniform width of the border around the pool

total area of pool AND border, %2830%2B2u%29%2840%2B2u%29

Area of just the pool, 30%2A40=1200

Area of just the border around pool, %2830%2B2u%29%2840%2B2u%29-30%2A40=296;
Simplify and solve for u.

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%2830%29%2840%29%2B2%2A40u%2B2%2A30u%2B4u%5E2-%2830%29%2840%29=296
2%2830%2B40%29u%2B4u%5E2=296
70u%2B2u%5E2=148
35u%2Bu%5E2=74
u%2835%2Bu%29=74-------------looking for two factors of 74, which differ by 35, highlight%28u=2%29 will fit this.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


No doubt a formal algebraic solution was expected for this problem.

However, note that solving the problem using logical reasoning and simple arithmetic (and, in this case, some common sense estimation) can be give good problem-solving experience.

The border will need to have strips along each of the four sides of the pool, which means along the whole perimeter, a distance of 2(30+40) = 140 feet.

We can estimate the width of the border by dividing the given 296 square feet of material by the perimeter of 140 feet to see that the width of the border will be about 2 feet.

The 2-foot border along all sides of the pool will use 140*2=280 square feet of the material.

And there will be square portions of the border at each corner of the pool that are each 2*2=4 square feet.

But 280 square feet of material along the edges of the pool, plus four corners of 4 square feet each makes exactly the 296 square feet we have. So

ANSWER: The border can be 2 feet wide.