AMC 10 · 2006 · #1

Grade 3 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Weighted Group Aggregation

ratemental-arithmeticorder-of-operations identify-subproblems ↑ Prerequisites: mental-arithmetic

📏 Short solution 💡 1 insight

📘 View easy version →

Problem

Each sandwich costs 3 dollars and each soda costs 2 dollars. Find the total cost of 5 sandwiches and 8 sodas.

Pick an answer.

(A)

(B)

(C)

(D)

(E)

How to solve

Strategy Analyze the Units

This is a money problem where each item has a price in dollars-per-item, so Tool #8 (Analyze the Units) says: multiply how many by the price each to get dollars. Tool #7 (Identify Subproblems) splits the order into two easy pieces — the cost of the sandwiches and the cost of the sodas — which are then added. Tool #3 (Eliminate Possibilities) gives a fast reality check: the choices are all near 30, and the two subtotals are 15 and 16, so the answer must sit at the low end.

1STEP 1

Cost of the sandwiches

The sandwiches come to 15.

5 ×

3 =

2STEP 2

Cost of the sodas

The sodas come to 16.

8 ×

2 =

3STEP 3

Add the two subtotals

Adding the subtotals gives 31, choice (A).

15 +

16 = $31 → (A)

Answer

A rough estimate confirms it: 5 sandwiches and 8 sodas is 13 items, and prices sit between

2 and

3, so the bill should land between 13 × 2 = 26 and 13 × 3 = 39 dollars — and 31 sits right in that window. The two subtotals

15 and

16 are each just under half of the total, and 15 + 16 = 31 checks out, so (A) is solid while (D) 34 and (E) 35 are too high.

💡Key takeaway

For a shopping bill, multiply each item's count by its price, then add the pieces together.

Cost of the sandwiches
Cost of the sodas
Add the two subtotals

Cost of the sandwiches

Cost of the sodas

Add the two subtotals

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