Question

Pablo 给他的朋友们买冰棒。商店出售单支冰棒，每支 $\$1$ ； $3$ 支装盒，每盒 $\$2$ ；以及 $5$ 支装盒，每盒 $\$3$ 。Pablo 用 $\$8$ 最多可以买多少支冰棒？

Pablo buys popsicles for his friends. The store sells single popsicles for $\$1$ each, $3$ -popsicle boxes for $\$2,$ and $5$ -popsicle boxes for $\$3.$ What is the greatest number of popsicles that Pablo can buy with $\$8?$

$8$

$11$

$12$

$13$

$15$

答案：D

知识点：最优化速率

难度评级：890

解答：

最便宜的冰棒来自 $5$ 支装盒，单价为 $\dfrac{\$3}{5}=\$0.60$ 。即使按这个单价， $14$ 支冰棒也要花 $14\cdot\$0.60=\$8.40$ ，超过 $\$8$ 。

因此 Pablo 最多能买 $13$ 支，而且他可以用 $\$6$ 买两盒 $5$ 支装，再用 $\$2$ 买一盒 $3$ 支装，得到 $2\cdot5+3=13$ 支冰棒。

所以正确答案是 D。

The cheapest popsicles come from the $5$ -popsicle box, at $\dfrac{\$3}{5}=\$0.60$ each. Even at that rate, $14$ popsicles would cost $14\cdot\$0.60=\$8.40,$ more than $\$8.$

So Pablo can buy at most $13,$ and he achieves this with two $5$ -boxes for $\$6$ and one $3$ -box for $\$2,$ giving $2\cdot5+3=13$ popsicles.

Thus, the correct answer is D.

2017 AMC 12A 第 1 题

答案：D

难度评级：890

解答：

其他年份的第 1 题