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2013 AMC 10A Problem 1

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2013 AMC 10A Problem 1AMC 10 Step by Step
Name:                             Date: October 28, 2026
Linear Equations & Word Problems · difficulty 1 of 5 · about 1 min · position P1-10

A taxi ride costs 1.50plus1.50 plus 0.25 per mile traveled. How much does a 5-mile taxi ride cost?

  1. A)2.252.25
  2. B)2.502.50
  3. C)2.752.75
  4. D)3.003.00
  5. E)3.753.75

Answer

C

Key insight

The 1.50 is paid once, but the 0.25 is paid again for every mile, so add 1.50 to 5 times 0.25.

Solution

The price has two parts, so work them out one at a time.

1. The part you always pay. Getting in the taxi costs $1.50\$1.50, no matter how far you go.
2. The part that grows with distance. Every mile adds $0.25\$0.25. For 55 miles that is
5×0.25=1.25 dollars.5 \times 0.25 = 1.25 \text{ dollars}.
3. Add the two parts.
1.50+1.25=2.75.1.50 + 1.25 = 2.75.

A quick check: $0.25\$0.25 is a quarter, and 55 quarters is $1.25\$1.25, which matches Step 2.

The ride costs (C) 2.75\boxed{\textbf{(C)}\ 2.75}.

Why this works

Many word problems have the shape "a fixed amount plus so much for each unit": taxi fares, phone plans, bike rentals. Find the number that is paid once and the number that gets multiplied by the quantity. Then multiply and add. A cost of 1.50+0.25×(miles)1.50 + 0.25 \times (\text{miles}) is an example of a linear formula, and this problem only asks you to put in 55 miles.

The trap

Adding 0.25 only once (getting 1.75) instead of paying it for each of the 5 miles.

Concise solution

The ride has two parts: a flat charge of $1.50\$1.50 that is paid regardless of distance, and a distance charge of $0.25\$0.25 for every mile.

Five miles cost 5×0.25=1.255 \times 0.25 = 1.25 dollars. Adding the flat charge:
1.50+1.25=2.75.1.50 + 1.25 = 2.75.

The ride costs (C) 2.75\boxed{\textbf{(C)}\ 2.75}.

Review in the AoPS books

Techniques

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