2008 AMC 10A Problem 12

Question

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

Write the blue and green counts in terms of

r

From

r = 1.25b

we get

b = 0.8r,

and

g = 1.6r

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.

Problem 12 in other years