Competition · AMC preparation · step 4 of 4
AMC 8 · 2011 · #1
Grade 4 arithmeticPick an answer.
AMC 8 2011 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The only catch in this problem is mixed units — cents for the apple price, dollars for the bill and the answer choices. Tool #8 (Analyze the Units) makes sure we convert 50 cents into 1.50) before subtracting. Tool #7 (Identify Subproblems) breaks the work into two clean pieces: first find the total cost of the apples, then subtract from $5 to get the change.
Find the apples' total cost
Total apple cost = apples × price each = 3 × 50 cents = 150 cents.
Multiplying "how many" by "price each" to get a total is the Grade 3 multiplication word-problem move.
3.OA.A.3Identify SubproblemsConvert cents to dollars
Convert to dollars to match the bill: 100 cents = $1, so 150 cents = $1.50.
Switching between cents and dollars within the same money system is the Grade 4 measurement-conversion skill.
4.MD.A.1Analyze The UnitsSubtract to find the change
Change = amount paid - total cost = $5.00 - $1.50 = $3.50, choice (E).
Change = paid - cost is the classic money word-problem subtraction at Grade 4.
Margie's change equals the money she paid minus the total cost of the apples.
▸ Why?
The money Margie handed over splits with no overlap into two parts — the part that pays for the apples and the part returned to her as change — so those two parts together make up the whole amount she paid.
▸ Why?
Because the cost and the change add up to the amount paid, finding the change means undoing that addition, and the operation that undoes adding is subtracting.
This AMC 8 problem only needs Grade 4 money sense — convert cents to dollars, then subtract — that you already know!
- Find the apples' total cost
- Convert cents to dollars
- Subtract to find the change
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