Question

Orvin 去商店时带的钱刚好够买 $30$ 个气球。到达后他发现商店正在特价：按原价买 $1$ 个气球，第二个气球可减免原价的 $\tfrac13$ 。Orvin 最多能买多少个气球？

Orvin went to the store with just enough money to buy $30$ balloons. When he arrived he discovered that the store had a special sale on balloons: buy $1$ balloon at the regular price and get a second at $\tfrac13$ off the regular price. What is the greatest number of balloons Orvin could buy?

$33$

$34$

$36$

$38$

$39$

答案：C

知识点：比与比例钱币

难度评级：1070

小提示：

把气球两两分组：一个按全价，另一个按原价的 $\tfrac23$ 。

Group the balloons into pairs, one at full price and one at $\tfrac23$ of the price

大提示：

每一组两个气球的费用是一个原价气球的 $\tfrac53$ 。

Each pair costs $\tfrac53$ of a regular balloon’s price

解答：

在特价下，一组两个气球的费用是一个原价气球的 $1 + \tfrac23 = \tfrac53$ 倍。

Orvin 的钱按原价可以买 $30$ 个气球，而按特价可以买 $30 \div \tfrac53 = 18$ 组，也就是 $36$ 个气球。

所以正确答案是 C。

Under the sale, a pair of balloons costs $1 + \tfrac23 = \tfrac53$ times the regular price of one balloon.

Orvin’s money buys $30$ balloons at the regular price, so he can afford $30 \div \tfrac53 = 18$ pairs, which is $36$ balloons.

Thus, the correct answer is C.

2014 AMC 12B 第 2 题

答案：C

难度评级：1070

小提示：

大提示：

解答：

其他年份的第 2 题