Question

一束花包含粉玫瑰、红玫瑰、粉康乃馨和红康乃馨。粉色花中有三分之一是玫瑰，红色花中有四分之三是康乃馨，且所有花中有十分之六是粉色。所有花中有百分之几是康乃馨？

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?

$15$

$30$

$40$

$60$

$70$

答案：E

知识点：分数百分数

难度评级：1100

解答：

所有花中十分之六是粉色，十分之四是红色。因为粉色花中三分之二是康乃馨，所以粉康乃馨占全部花的 $\tfrac{2}{3}\cdot\tfrac{6}{10} = \tfrac{4}{10}$ 。

因为红色花中四分之三是康乃馨，所以红康乃馨占全部花的 $\tfrac{3}{4}\cdot\tfrac{4}{10} = \tfrac{3}{10}$ 。康乃馨合计占 $\tfrac{4}{10} + \tfrac{3}{10} = \tfrac{7}{10} = 70\%$ 。

因此，正确答案是 E。

Six tenths of the flowers are pink and four tenths are red. Since two thirds of the pink flowers are carnations, pink carnations make up $\tfrac{2}{3}\cdot\tfrac{6}{10} = \tfrac{4}{10}$ of the flowers.

Since three fourths of the red flowers are carnations, red carnations make up $\tfrac{3}{4}\cdot\tfrac{4}{10} = \tfrac{3}{10}$ of the flowers. Together the carnations are $\tfrac{4}{10} + \tfrac{3}{10} = \tfrac{7}{10} = 70\%.$

Thus, the correct answer is E.

2013 AMC 12A 第 3 题

答案：E

难度评级：1100

解答：

其他年份的第 3 题