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2004 AMC 10A Problem 3

2004 AMC 10A Problem 3AMC 10 Step by Step

Name: Date: September 13, 2026

Ratios, Percents & Averages · difficulty 1 of 5 · about 1 min · position P1-10

Alicia earns 20 dollars per hour, of which $1.45\%$ is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes?

A)
$0.0029$
B)
$0.029$
C)
$0.29$
D)
$2.9$
E)
$29$

Answer

Key insight

Convert 20 dollars to 2000 cents first; 1.45 percent of 2000 is 29.

Solution

The question asks for cents, so express the wage in cents before taking the percentage: $20$ dollars is $2000$ cents.

Now $1.45\% = 0.0145$ , and
$0.0145 \times 2000 = 29.$

The tax withheld is $29$ cents per hour, so the answer is $\boxed{\textbf{(E)}\ 29}$ .

Why this works

Percent problems are a multiplication by a decimal; the only decision is which unit to multiply. Converting to the requested unit at the start avoids a factor-of- $100$ error at the end. Note that the answer choices differ only by powers of $10$ , which is a signal that the whole problem is about units.

Alternative approach

Sanity check with size: $1\%$ of $2000$ cents is $20$ cents, so $1.45\%$ should be a bit more than $20$ cents. Only choice (E) is in that range.

The trap

Computing 1.45 percent of 20 dollars and reporting 0.29 (dollars) as if it were cents, choice (C).

Common mistakes

Computing 1.45 percent of 20 dollars and reporting 0.29 (dollars) as if it were cents, choice (C).
Treating $1.45\%$ as $0.145$ or $1.45$ when converting to a decimal.

Techniques

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