AMC 8 · 2011 · #1
Grade 4 arithmeticProblem
Margie bought apples at a cost of cents per apple. She paid with a 5-dollar bill. How much change did Margie receive?
Pick an answer.
Toolkit + CCSS Solution
Understand
Restated: Margie buys $3$ apples that cost $50$ cents each and pays with a $\$5$ bill. How much change does she get back?
Givens: Number of apples bought $= 3$; Price per apple $= 50$ cents; Amount paid $= \$5$ bill; Answer choices: (A) $\$1.50$, (B) $\$2.00$, (C) $\$2.50$, (D) $\$3.00$, (E) $\$3.50$
Unknowns: The amount of change Margie receives, in dollars
Understand
Restated: Margie buys $3$ apples that cost $50$ cents each and pays with a $\$5$ bill. How much change does she get back?
Givens: Number of apples bought $= 3$; Price per apple $= 50$ cents; Amount paid $= \$5$ bill; Answer choices: (A) $\$1.50$, (B) $\$2.00$, (C) $\$2.50$, (D) $\$3.00$, (E) $\$3.50$
Plan
Primary tool: #8 Analyze the Units
Secondary: #7 Identify Subproblems
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 $\$0.50$ (or $150$ 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.
Execute — Answer: E
3.OA.A.3 Step 1 - Find the total cost of the apples.
- Three apples at $50$ cents each is a multiplication: number of apples times cost per apple.
💡 Multiplying "how many" by "price each" to get a total is the Grade 3 multiplication word-problem move.
4.MD.A.1 Step 2 Convert the total cost from cents to dollars so it matches the units of the $\$5$ bill. Since $100$ cents $= \$1$, $150$ cents $= \$1.50$.
💡 Switching between cents and dollars within the same money system is the Grade 4 measurement-conversion skill.
4.MD.A.2 Step 3 Subtract the total cost from the amount paid to find the change.
💡 Change $=$ paid $-$ cost is the classic money word-problem subtraction at Grade 4.
3.OA.A.3 Find the total cost of the apples. Three apples at $50$ cents each is a multipli 4.MD.A.1 Convert the total cost from cents to dollars so it matches the units of the $\$5 4.MD.A.2 Subtract the total cost from the amount paid to find the change. Review
Reasonableness: Three apples at about $50$ cents each is around $\$1.50$ total, which is much less than $\$5$, so the change should be most of the bill — closer to $\$3.50$ than to $\$1.50$. The answer (E) $\$3.50$ fits that estimate exactly.
Alternative: Tool #6 (Guess and Check) on the choices: if the change were $\$3.50$, then the apples cost $\$5.00 - \$3.50 = \$1.50$, i.e. $50$ cents each — which matches the problem. The other choices give apple totals of $\$3.50$, $\$3.00$, $\$2.50$, $\$2.00$, none of which equal $3 \times \$0.50$.
CCSS standards used (min grade 4)
3.OA.A.3Use multiplication and division within $100$ to solve word problems (Multiplying $3 \times 50 = 150$ cents to find the total cost of the apples.)4.MD.A.1Convert measurements from a larger unit to a smaller unit within the same measurement system (Converting $150$ cents into $\$1.50$ so the total cost and the payment use the same unit.)4.MD.A.2Solve word problems involving distances, time, liquid volumes, masses, and money (Subtracting $\$5.00 - \$1.50 = \$3.50$ to find Margie's change in a money word problem.)
⭐ This AMC 8 problem only needs Grade 4 money sense — convert cents to dollars, then subtract — that you already know!
⭐ This AMC 8 problem only needs Grade 4 money sense — convert cents to dollars, then subtract — that you already know!
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