AMC 8 · 2006 · #1

Easy mode Grade 5

Problem

Imagine Mindy went shopping and bought three things. The three prices were $\textdollar 1.98$ , $\textdollar 5.04$ , and $\textdollar 9.89$ .

Add the three prices to get her total. Then round that total to the nearest whole dollar.

What is the rounded total?

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

Add the three prices

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

Round to the nearest dollar

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.

Toolkit + CCSS Solution

Understand

Plan

Execute — Answer: D

Add the three prices

Round to the nearest dollar

Review

CCSS standards used (min grade 5)

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