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2008 AMC 10B Problem 18

Problem 18 of 25IntermediateAlgebraArithmetic

Bricklayer Brenda would take 99 hours to build a chimney alone, and bricklayer Brandon would take 1010 hours to build it alone. When they work together, they talk a lot, and their combined output is decreased by 1010 bricks per hour. Working together, they build the chimney in 55 hours. How many bricks are in the chimney?

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Solution

Let nn be the number of bricks. Brenda lays n9\tfrac{n}{9} per hour and Brandon n10,\tfrac{n}{10}, so together they lay n9+n10−10\tfrac{n}{9}+\tfrac{n}{10}-10 per hour. Over 55 hours this equals n:n: 5(n9+n10−10)=n.5\left(\tfrac{n}{9}+\tfrac{n}{10}-10\right)=n. Solving, 5n9+n2−50=n,\tfrac{5n}{9}+\tfrac{n}{2}-50=n, which gives n=900.n=900. Thus, the correct answer is B.
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