An item costs 35¢. A customer pays with 50¢. The cashier hands back 35¢, saying 'that's what the item cost.' What error did the cashier make?
AThe cashier added the price and payment together instead of subtracting
BThe cashier confused the price with the amount of change — change is 50 − 35 = 15¢, not 35¢
CThe cashier subtracted in the wrong direction, computing 35 − 50 instead of 50 − 35
DThe cashier should only accept exact change to avoid this kind of error
The cashier made the classic error of confusing the price with the change. The price (35¢) is what the store keeps. The change is what the store returns — only the difference between what was paid (50¢) and what was owed (35¢). Change = 50 − 35 = 15¢. The customer paid 15¢ more than the item cost, so only 15¢ is returned, not 35¢.
Question 2 Multiple Choice
Which equation correctly calculates the change when an item costs 42¢ and the customer pays 75¢?
A42 + 75 = 117¢
B42 − 75 = −33¢
C75 − 42 = 33¢
D75 + 42 = 117¢
Change = amount paid − price = 75 − 42 = 33¢. The direction is always payment minus price, because the customer paid more than the item costs and receives the excess back. Option B (42 − 75) subtracts in the wrong direction, giving a negative number — which tells you the customer didn't pay enough, the opposite situation. Change is always a positive number when the customer paid at least the price.
Question 3 True / False
If you pay for a 28¢ item with a 50¢ coin, your change is 28¢.
TTrue
FFalse
Answer: False
The change is 50 − 28 = 22¢, not 28¢. The confusion here is mixing up the price (28¢) with the amount of change. The price is what the store keeps. The change is only the excess — how much more you paid than the item costs. Since you paid 50¢ and owed 28¢, the store keeps 28¢ and returns 22¢. Checking: 28 + 22 = 50 ✓.
Question 4 True / False
Counting up from the price to the amount paid gives the same answer as subtracting the price from the amount paid.
TTrue
FFalse
Answer: True
Both strategies find the same difference — just by moving in opposite directions. Subtracting: 50 − 28 = 22¢. Counting up: start at 28, hop to 30 (+2), hop to 50 (+20), total = 22¢. They must give the same answer because change is defined as the difference between payment and price, and subtraction and counting up are two different ways to find that same difference.
Question 5 Short Answer
An item costs 46¢ and the customer pays 60¢. Find the change using both strategies — subtraction and counting up — and explain why they give the same answer.
Think about your answer, then reveal below.
Model answer: Subtraction: 60 − 46 = 14¢. Counting up: start at 46, add 4 to reach 50 (a friendly ten), then add 10 to reach 60. Total added: 4 + 10 = 14¢. They give the same answer because both are finding the gap between 46 and 60 — the size of the difference. Subtraction computes it directly; counting up builds it by collecting hops. The difference between two numbers is the same no matter which direction you measure it from.
This dual-strategy understanding is the heart of making change. Many experienced cashiers count up naturally because hops to friendly tens are easier to track mentally. But the arithmetic is identical — both methods answer the question 'how far apart are these two amounts?' Knowing both strategies lets you choose whichever is easier for a given problem and gives you a way to check your answer.