2008 AMC 10A Problem 12

Below is the professionally curated solution for Problem 12 of the 2008 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 10A solutions, or check the answer key.

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Concepts:percentage algebraic manipulation

Difficulty rating: 1260

12.

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

$2.85r$

$3r$

$3.4r$

$3.85r$

$4.25r$

Solution:

Since $r = 1.25b,$ the number of blue marbles is $b = \dfrac{r}{1.25} = 0.8r.$

The number of green marbles is $g = 1.6r.$

The total is $r + 0.8r + 1.6r = 3.4r.$

Thus, the correct answer is C.

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