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2013 AMC 10A Problem 1

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2013 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

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

A)
$2.25$
B)
$2.50$
C)
$2.75$
D)
$3.00$
E)
$3.75$

Answer

Key insight

The fare is a fixed 1.50 plus 0.25 for each of the 5 miles, so add 1.50 and 5 times 0.25.

Solution

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

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

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

Why this works

A "fixed fee plus rate per unit" description is a linear function $c(m) = 1.50 + 0.25m$ . Identify which number is the constant and which one gets multiplied by the quantity, then evaluate. This is the same structure as phone bills, rentals, and every other "base plus per-unit" word problem.

The trap

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

Common mistakes

Adding the 0.25 only once (giving 1.75) instead of charging it for each of the 5 miles.
Multiplying the flat fee by the number of miles ( $5 \times 1.50$ ) instead of the per-mile rate.

Techniques

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