Question

三袋软糖分别有 $26$ ， $28$ 和 $30$ 颗。这三袋中黄色软糖所占比例分别为 $50\%$ 、 $25\%$ 和 $20\%$ 。把三袋糖全部倒入一个碗中，黄色软糖占碗中所有软糖的比例最接近下列哪一个？

Three bags of jelly beans contain $26,$ $28,$ and $30$ beans. The ratios of yellow beans to all beans in each of these bags are $50\%,$ $25\%,$ and $20\%,$ respectively. All three bags of candy are dumped into one bowl. Which of the following is closest to the ratio of yellow jelly beans to all beans in the bowl?

$31\%$

$32\%$

$33\%$

$35\%$

$95\%$

答案：A

知识点：百分数平均数

难度评级：1150

小提示：

用黄色软糖总数除以软糖总数

Divide total yellow beans by total beans

大提示：

先求每袋中黄色软糖的颗数

Find the number of yellow beans in each bag

解答：

第一袋中有 $26 \cdot 0.5 = 26 \div 2 = 13$ 颗黄色软糖，第二袋中有 $28 \cdot 0.25 = 28 \div 4 = 7$ 颗黄色软糖，第三袋中有 $30 \cdot 0.2 = 30 \div 5 = 6$ 颗黄色软糖。

黄色软糖总数为 $13 + 7 + 6 = 26\text{，}$ 软糖总数为 $26 + 28 + 30 = 84\text{。}$ 黄色软糖所占的百分比为 $\dfrac{26}{84} \cdot 100 \% = \dfrac{13}{42} \cdot 100 \%$ $\approx 30.9 \%\text{。}$

所以正确答案是 A。

There are $26 \cdot 0.5 = 26 \div 2 = 13$ yellow jelly beans in the first bag, $28 \cdot 0.25 = 28 \div 4 = 7$ yellow jelly beans in the second bag, and $30 \cdot 0.2 = 30 \div 5 = 6$ yellow jelly beans in the third bag.

The total number of yellow jelly beans is $13 + 7 + 6 = 26$ and the total number of jelly beans is $26 + 28 + 30 = 84.$ The ratio of yellow jelly beans to all the beans is $\dfrac{26}{84} \cdot 100 \% = \dfrac{13}{42} \cdot 100 \%$ $\approx 30.9 \%.$

Thus, A is the correct answer.

1997 AMC 8 第 13 题

答案：A

难度评级：1150

小提示：

大提示：

解答：

其他年份的第 13 题