PSAT Math Multiple-Choice Question 423: Answer and Explanation

Question: 423

Tyree is dropping old pennies into a jar that contains a cleaning solution. As he adds more pennies, the height of the solution in the jar changes based on the number of pennies he adds. The figure shows this relationship after 50 pennies have been dropped in the jar. If the height of the solution in the jar was 5 inches (in) before any pennies were added, which of the following linear functions represents the relationship between the number of pennies, p, and the height in inches, h(p), of the solution in the jar?

• A. h(p) = 0.7p + 5
• B. h(p) = 0.7p + 8.5
• C. h(p) = 0.07p + 5
• D. h(p) = 0.07p + 8.5

Correct Answer: C

Explanation:

C

Difficulty: Medium

Strategic Advice: The question tells you that the function is linear, which means you need to know the slope (rate of change in the height of the solution) and the y-intercept (height of the solution when there are 0 pennies) to pick the correct function.

Getting to the Answer: You already know the height of the solution when there are 0 pennies—it's 5 inches. This means you can eliminate (B) and (D). To determine the rate of change in the height of the solution, write what you know as ordered pairs, and then use the slope formula:

At 0 pennies, the height is 5 inches → (0, 5).

At 50 pennies, the height is 8.5 inches → (50, 8.5).

The rate of change in the height of the solution is This means the correct function is h(p) = 0.07p + 5, which is (C).