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2006 AMC 10A Problem 1

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2006 AMC 10A Problem 1AMC 10 Step by Step
Name:                             Date: September 13, 2026
Linear Equations & Word Problems · difficulty 1 of 5 · about 1 min · position P1-10

Sandwiches at Joe's Fast Food cost $3\$3 each and sodas cost $2\$2 each. How many dollars will it cost to purchase 55 sandwiches and 88 sodas?

  1. A)

    3131

  2. B)

    3232

  3. C)

    3333

  4. D)

    3434

  5. E)

    3535

Answer

A

Key insight

Cost is quantity times unit price for each item, then add: 5 times 3 plus 8 times 2.

Solution

Five sandwiches at $3\$3 apiece come to 5⋅3=155 \cdot 3 = 15 dollars. Eight sodas at $2\$2 apiece come to 8⋅2=168 \cdot 2 = 16 dollars.

Adding the two subtotals gives 15+16=3115 + 16 = 31 dollars.

The answer is (A) 31\boxed{\textbf{(A)}\ 31}.

Why this works

A purchase of several kinds of items costs the sum of (quantity ×\times unit price) over the kinds. Keeping each product on its own line before adding is the whole technique; it also makes it easy to check that each price was paired with the right count.

The trap

Pairing the prices with the wrong items (5 times 2 plus 8 times 3 = 34, choice (D)).

Common mistakes

  • Pairing the prices with the wrong items (5 times 2 plus 8 times 3 = 34, choice (D)).
  • Adding the numbers of items or the prices instead of multiplying, e.g. 5+8+3+25 + 8 + 3 + 2.

Techniques

Set up the equation/formula and compute; no special trick needed