¶ 2022 AMC8 Problem 15
Problem:
László 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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The dashed line in the figure above passes through the peppers that cost exactly per ounce. The peppers above the line are more expensive. The only peppers that cost less than per ounce are the three peppers below the dashed line, labeled and . Pepper costs about for ounces, which is per ounce; pepper costs a little less than per ounce; and pepper costs about for ounces, which is per ounce. Thus the lowest price per ounce is offered by pepper which weighs ounces.
If a line is drawn from the origin to any of the peppers, the slope of the line corresponds to the price per ounce for that pepper. The line with the smallest slope, as shown above, is the one connecting the origin to pepper , which weighs ounces.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions