Questions: Making Change and Money Word Problems

Question 1

Marcus buys a pencil for 45¢ and pays with 2 quarters. How much change does he get?

• A. 5¢ — 50¢ minus 45¢
• B. 45¢ — the price of the pencil
• C. 95¢ — the price plus the amount paid
• D. 10¢ — subtracting the quarters from the price

Answer: (A)

Change = amount paid − price = 50¢ − 45¢ = 5¢. Two quarters = 50¢ (each quarter = 25¢). The price is 45¢. The subtraction is straightforward once you correctly identify both amounts. Option B confuses the price with the change; option C adds instead of subtracts; option D performs the subtraction backwards.

Question 2

In the problem 'Lily buys stickers for 63¢ and pays with 3 quarters. How much change does she get?' — what is the unknown quantity?

• A. The price of the stickers
• B. The number of quarters Lily used
• C. The amount of change she receives
• D. The total value of 3 quarters

Answer: (C)

Identifying the unknown is the first step in solving any word problem. The price (63¢) is given. The number of quarters (3) is given. The total value of 3 quarters (75¢) can be calculated from given information. What the problem asks for — and what is not directly stated — is the change. Translating 'how much change' into 'amount paid minus price' is the key move: 75¢ − 63¢ = 12¢.

Question 3

Counting up from the price to the amount paid gives a different answer than subtracting the price from the amount paid.

• T. True
• F. False

Answer: False

Both methods measure the same gap between two numbers — they are mathematically identical. Counting up from 37¢ to 50¢ (add 3¢ to reach 40¢, add 10¢ to reach 50¢, total = 13¢) gives the same answer as 50 − 37 = 13. Counting up mirrors the physical action of making change at a register; subtraction is the arithmetic abstraction of the same operation. Same result, different mental approach.

Question 4

To find the change owed, you subtract the price from the amount paid.

• T. True
• F. False

Answer: True

Change = amount paid − price. If you pay more than the item costs, the difference comes back to you. This direction of subtraction matters: the amount paid is the larger number, and the price is subtracted from it. Reversing the subtraction (price − amount paid) would give a negative number, which signals you've set it up backwards.

Question 5

Why is 'translating the situation into a calculation' the key skill in money word problems? Give an example of a translation step you would need to take.

Model answer: Word problems describe a real situation using language — your job is to convert that language into the numbers and operations needed to solve it. The arithmetic itself is often simple; the difficulty is identifying what is known, what is unknown, and which operation connects them. Example: 'Mia pays with 3 quarters' must be translated to '3 × 25¢ = 75¢ paid' before you can subtract the price.

Students often struggle with money word problems not because of the arithmetic but because they cannot extract the right numbers and operation from the sentence. The translation habit — pausing to name the price, name the amount paid, identify what's missing, then choose the operation — applies to all applied math, not just money. Every real-world math problem requires this interpretation step before any calculation begins.