AMC10 2013 A

AMC10 2013 A · Q10

AMC10 2013 A · Q10. It mainly tests Fractions, Ratios & proportions.

A flower bouquet contains pink roses, red roses, pink carnations, and red carnations. One third of the pink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations?

一个花束包含粉色玫瑰、红色玫瑰、粉色康乃馨和红色康乃馨。粉色花中的三分之一是玫瑰，红色花中的四分之三是康乃馨，花束中有十分之六是粉色花。花束中有百分之多少是康乃馨？

(A) 15 15

(B) 30 30

(D) 60 60

(E) 70 70

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): Because six tenths of the flowers are pink and two thirds of the pink flowers are carnations, $\frac{6}{10}\cdot\frac{2}{3}=\frac{2}{5}$ of the flowers are pink carnations. Because four tenths of the flowers are red and three fourths of the red flowers are carnations, $\frac{4}{10}\cdot\frac{3}{4}=\frac{3}{10}$ of the flowers are red carnations. Therefore $\frac{2}{5}+\frac{3}{10}=\frac{7}{10}=70\%$ of the flowers are carnations.

答案（E）：因为十分之六的花是粉色的，且粉色花中有三分之二是康乃馨，所以 $\frac{6}{10}\cdot\frac{2}{3}=\frac{2}{5}$ 的花是粉色康乃馨。因为十分之四的花是红色的，且红色花中有四分之三是康乃馨，所以 $\frac{4}{10}\cdot\frac{3}{4}=\frac{3}{10}$ 的花是红色康乃馨。因此 $\frac{2}{5}+\frac{3}{10}=\frac{7}{10}=70\%$ 的花是康乃馨。

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