AMC 8 · 2011 · #1

Grade 4 arithmetic
Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation
multi-digit-arithmeticunit-conversionmental-arithmetic identify-subproblemsdimensional-analysis ↑ Prerequisites: multi-digit-arithmetic
📏 Short solution 💡 2 insights
📘 View easy version →
Problem
Margie buys 3 apples that cost 50 cents each and pays with a $5 bill. How much change does she get back?

Pick an answer.

(A)
$\textdollar 1.50$
(B)
$\textdollar 2.00$
(C)
$\textdollar 2.50$
(D)
$\textdollar 3.00$
(E)
$\textdollar 3.50$

AMC 8 2011 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve
Strategy Analyze the Units

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(or150centsinto0.50 (or 150 cents into1.50) 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.

1STEP 1

Total apple cost = apples × price each = 3 × 50 cents = 150 cents.

3 × 50 cents = 150 cents
2STEP 2

Convert to dollars to match the bill: 100 cents = 1,so150cents=<spanclass="mk−a"><spanclass="hl−ask">1, so 150 cents = <span class="mk-a"><span class="hl-ask">1.50.

150 cents × 1/(100cents)=1/(100 cents) =1.50
3STEP 3

Change = amount paid - total cost = 5.00−5.00 -1.50 = $3.50, choice (E).

5.00−5.00 -1.50 = $3.50 → (E)
Answer
textdollar 3.50
Three apples at about 50 cents each is around 1.50total,whichismuchlessthan1.50 total, which is much less than5, so the change should be most of the bill — closer to 3.50thanto3.50 than to1.50. The answer (E) $3.50 fits that estimate exactly.
💡Key takeaway

This AMC 8 problem only needs Grade 4 money sense — convert cents to dollars, then subtract — that you already know!

More like this

Same archetype — closest grade level first.