PSAT Math Multiple-Choice Question 554: Answer and Explanation

Question: 554

Hannah has only nickels and dimes in her wallet. She has a total of $2.50 and a total of
30 coins. How many nickels does she have

• A. 10
• B. 12
• C. 15
• D. 16

Correct Answer: A

Explanation:

(A) Set up a series of two equations. Put everything in terms of cents for sake of simplicity. Use N as the number of nickels and D as the number of dimes:

The total number of coins: N + D = 30

The total number of cents: 5N + 10 D = 250

Express D in terms of N based on the first equation:

N + D = 30

D = 30 - N

Then, substitute this for D in the second equation:

5N + 10 D = 250

5N + 10(30 - N) = 250

5N + 300 -10N = 250

-5N = -50

N = 10

Alternatively, you can solve this by working backward from the answers. Since the total number of cents must be 250, try the different possible values of nickels from the choices to see which one works. You can try choice (B) or choice (C) since they are in the middle. Once you get to choice (A), you will find that if you have 10 nickels, you have 50 cents from nickels. That means there must be 200 cents from dimes, which also means there are 20 dimes. Since 20 dimes and 10 nickels add together to give you 30 coins total, choice (A) is correct.