AMC 8 · 2006 · #1

Grade 5 arithmetic
Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation
estimationmulti-digit-arithmeticfraction-decimal-conversion identify-subproblems ↑ Prerequisites: multi-digit-arithmeticplace-value
📏 Short solution 💡 2 insights
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Problem
Mindy made three purchases of 1.98</span>,<spanclass="mk−c">1.98</span>, <span class="mk-c"> 5.04, and $ 9.89. What is her total cost, rounded to the nearest dollar?

Pick an answer.

(A)
10
(B)
15
(C)
16
(D)
17
(E)
18

AMC 8 2006 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve
Strategy Break into Subproblems

The question hides two separate tasks behind one sentence, so Tool #7 (Break into Subproblems) is the natural fit: (i) add the three prices to get the exact total, (ii) round that total to the nearest dollar. Doing them one at a time keeps the arithmetic clean. Tool #9 (Solve an Easier Related Problem) is the shortcut: because the question only asks for the nearest dollar, rounding each price first makes the addition trivial — as long as the rounding error stays small enough not to flip the final dollar.

1STEP 1

Add the three exact prices, lining up the decimal points: the total is 16.91.

1.98 + 5.04 + 9.89 = 16.91
2STEP 2

Round 16.91 to the nearest dollar: the tenths digit 9 is ≥ 5, so round up to 17.

16.91 ≈ 17 → (D)
Answer
17
Quick sanity check: the three prices are roughly 2,2, 5, 10,whichalreadysumto10, which already sum to 17 — exactly answer (D). The exact total 16.91 is only 9 cents short of 17, well within rounding range, so (D) is locked in. Choice (C) 16 would require the total to be under $ 16.50, but 16.91 ＞ 16.50, so (C) is ruled out.
💡Key takeaway

When a question asks for "nearest dollar," you don't need pinpoint cents — rounding each price first (2 + 5 + 10 = 17) often gets you straight to the answer, and the exact sum just confirms it.

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