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 for $\textdollar 1.98$ dollars, $\textdollar 5.04$ dollars, and $\textdollar 9.89$ dollars. What was her total, to the nearest dollar?

Pick an answer.

(A)

(B)

(C)

(D)

(E)

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

Try it yourself first — the explanation is most useful after you’ve attempted it.

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Toolkit + CCSS Solution

Understand

Restated: Mindy made three purchases of $\textdollar 1.98$, $\textdollar 5.04$, and $\textdollar 9.89$. What is her total cost, rounded to the nearest dollar?

Givens: Three prices: $\textdollar 1.98$, $\textdollar 5.04$, $\textdollar 9.89$; Answer choices: (A) $10$, (B) $15$, (C) $16$, (D) $17$, (E) $18$

Unknowns: The total cost rounded to the nearest whole dollar

Understand

Restated: Mindy made three purchases of $\textdollar 1.98$, $\textdollar 5.04$, and $\textdollar 9.89$. What is her total cost, rounded to the nearest dollar?

Givens: Three prices: $\textdollar 1.98$, $\textdollar 5.04$, $\textdollar 9.89$; Answer choices: (A) $10$, (B) $15$, (C) $16$, (D) $17$, (E) $18$

Plan

Primary tool: #7 Break into Subproblems

Secondary: #9 Solve an Easier Related Problem

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.

Execute — Answer: D

#7 Break into Subproblems 5.NBT.B.7 Step 1

Subproblem 1: add the three exact prices.
Line up the decimals and add column by column.

$$1.98 + 5.04 + 9.89 = 16.91$$

💡 Adding decimals to the hundredths place is a Grade 5 skill — line up the decimal points and carry as usual.

#7 Break into Subproblems 5.NBT.A.4 Step 2

Subproblem 2: round $16.91$ to the nearest dollar.
Look at the tenths digit.
It is $9$, which is $\geq 5$, so round up from $16$ to $17$.

$$16.91 \approx 17 \;\Rightarrow\; \textbf{(D)}$$

💡 Standard rounding rule: tenths digit $\geq 5$ means round up. $16.91$ is much closer to $17$ than to $16$.

[1] #7 5.NBT.B.7 Subproblem 1: add the three exact prices. Line up the decimals and add column by

[2] #7 5.NBT.A.4 Subproblem 2: round $16.91$ to the nearest dollar. Look at the tenths digit. It

Review

Reasonableness: Quick sanity check: the three prices are roughly $\textdollar 2$, $\textdollar 5$, $\textdollar 10$, which already sum to $\textdollar 17$ — 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 $\textdollar 16.50$, but $16.91 > 16.50$, so (C) is ruled out.

Alternative: Tool #9 (Solve an Easier Related Problem): round each price first, then add. $1.98 \approx 2$, $5.04 \approx 5$, $9.89 \approx 10$, giving $2 + 5 + 10 = 17$. The rounding errors are $+0.02, -0.04, +0.11$, summing to $+0.09$, which is far less than $\$0.50$, so rounding first cannot flip the answer. Still (D).

CCSS standards used (min grade 5)

5.NBT.A.4 Use place value understanding to round decimals to any place (Rounding $16.91$ to the nearest whole dollar by checking the tenths digit.)
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths (Adding $1.98 + 5.04 + 9.89 = 16.91$ with decimals aligned to the hundredths place.)

⭐ 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.

Problem

Toolkit + CCSS Solution

Understand

Plan

Execute — Answer: D

Review

CCSS standards used (min grade 5)

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