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2008 AMC 10A Problem 12

Problem 12 of 25IntermediateAlgebra

In a collection of red, blue, and green marbles, there are 25%25\% more red marbles than blue marbles, and there are 60%60\% more green marbles than red marbles. Suppose that there are rr red marbles. What is the total number of marbles in the collection?

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Solution

Since r=1.25b,r = 1.25b, the number of blue marbles is b=r1.25=0.8r.b = \dfrac{r}{1.25} = 0.8r. The number of green marbles is g=1.6r.g = 1.6r. The total is r+0.8r+1.6r=3.4r.r + 0.8r + 1.6r = 3.4r. Thus, the correct answer is C.

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Concepts: percentage · algebraic manipulation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.