AMC10 2008 A

AMC10 2008 A · Q12

AMC10 2008 A · Q12. It mainly tests Ratios & proportions.

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?

在一组红、蓝、绿弹珠中，红弹珠比蓝弹珠多25%，绿弹珠比红弹珠多60%。假设有$r$个红弹珠。集合中弹珠总数是多少？

(A) 2.85$r$ 2.85$r$

(B) 3$r$ 3$r$

(D) 3.85$r$ 3.85$r$

(E) 4.25$r$ 4.25$r$

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Let $b$ and $g$ represent the number of blue and green marbles, respectively. Then $r=1.25b$ and $g=1.6r$. Thus the total number of red, blue, and green marbles is $$ r+b+g=r+\frac{r}{1.25}+1.6r=r+0.8r+1.6r=3.4r. $$

答案（C）：令 $b$ 和 $g$ 分别表示蓝色和绿色弹珠的数量。则 $r=1.25b$ 且 $g=1.6r$。因此红色、蓝色和绿色弹珠的总数为 $$ r+b+g=r+\frac{r}{1.25}+1.6r=r+0.8r+1.6r=3.4r。 $$

Topics

AR.004 Ratios & proportions