Question

Laszlo 上网购买黑胡椒，找到了三十种不同的黑胡椒选项，重量和价格如下方散点图所示。按盎司计算，哪种重量的黑胡椒每盎司价格最低？

Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?

$1$

$2$

$3$

$4$

$5$

答案：C

知识点：数据与图表解读斜率最优化

难度评级：1140

解答：

每种重量只可能由该重量下价格最低的点成为最优。

在 $1$ 盎司时，最低价格超过 $1$ 美元，所以每盎司价格超过 $1$ 美元。

在 $2$ 盎司时，最低价格为 $2$ 美元，所以每盎司价格为 $1$ 美元。

在 $3$ 盎司时，最低价格约为 $2.5$ 美元，所以每盎司价格约为 $\frac{2.5}{3}$ ，小于 $1$ 美元。

在 $4$ 盎司时，最低价格接近 $3.9$ 美元，每盎司约为 $\frac{3.9}{4}$ ，仍高于 $3$ 盎司选项。

在 $5$ 盎司时，最低价格接近 $4.5$ 美元，每盎司约为 $\frac{4.5}{5}$ ，也高于 $3$ 盎司选项。

所以每盎司价格最低的是 $3$ 盎司。

正确答案是 C。

For each weight, only the lowest-price point at that weight can give the lowest price per ounce.

At $1$ ounce, the lowest price is more than $1$ dollar, so the price per ounce is more than $1$ .

At $2$ ounces, the lowest price is $2$ dollars, so the price per ounce is $1$ .

At $3$ ounces, the lowest price is about $2.5$ dollars, so the price per ounce is about $\frac{2.5}{3}$ , less than $1$ .

At $4$ ounces, the lowest price is close to $3.9$ dollars, so the price per ounce is close to $\frac{3.9}{4}$ , still larger than the $3$ -ounce option.

At $5$ ounces, the lowest price is close to $4.5$ dollars, so the price per ounce is close to $\frac{4.5}{5}$ , also larger than the $3$ -ounce option.

The price per ounce is lowest at $3$ ounces.

Thus, the correct answer is C.

2022 AMC 8 第 15 题

答案：C

难度评级：1140

解答：

其他年份的第 15 题