PSAT Math Multiple-Choice Question 747: Answer and Explanation

Question: 747

A convenience store has a "change bowl" on its counter in which there can be 5-cent nickels and/or 1-cent pennies. The store manager insists that whenever there is a dollar (100 cents) or more in the bowl, some change must be removed. What expression gives range of P pennies and N nickels that could be in the change bowl at any given time without the cashier needing to remove any coins?

• A. 100P - N > 5
• B. 6(P + N) < 100
• C. 0.01P + 0.05N < 100
• D. P + 5N < 100

Correct Answer: D

Explanation:

(D) Each penny is worth 1 cent, and each nickel is worth 5 cents. So the total number of cents given by the total coins in the change bowl is P + 5N. This needs to be less than 1 dollar total, i.e., 100 cents. So the inequality P + 5N < 100 is the solution.