PSAT Math Multiple-Choice Question 622: Answer and Explanation

Question: 622

Susan is given a piggybank for her birthday that can hold a maximum of 500 quarters. The piggy­bank initially has 120 quarters. Each day after she receives the bank, 4 quarters are added. No coins or other objects are added to the piggybank. Which equation could be used to solve for the number of days (D) after Susan's birthday that it will take to fill the bank?

• A. 500 = 120 + 4D
• B. 500 = 4D - 120
• C. 120 = 4D
• D. 500 = 4 + 120D

Correct Answer: A

Explanation:

(A) When the piggybank is full, it will have 500 quarters in it. Let's write an expression for how many quarters the piggybank contains on any given day, D, after Susan's birthday.

Susan starts with 120 quarters on day 0 (her birthday), so 120 is a constant. Every day, 4 quarters are added to the bank. Thus, on day 1, 4 quarters have been added. On day 2, Susan adds an additional 4 quarters to the bank so that 4(2) = 8 quarters total have been added since her birthday. On day 3, 4(3) = 12 quarters total have been added, and so on. This part of the expression can be written as 4D.

Adding in the original 120 quarters she started with gives an expression for the total number of quarters in the bank D days after Susan's birthday:

120 + 4D

We know the bank is full when it contains 500 quarters. So we can set our expression equal to 500 and solve for D to determine how many days after Susan's birthday the piggybank will be filled. Thus choice (A), 500 = 120 + 4D, is correct.