2026 AMC 10A Problem 2

A percent always means "percent of something". The $27\%$ tax is $27\%$ of the parking price before tax. The question asks what percent the tax is of the total, which is a bigger number. So the answer has to be smaller than $27\%$.

1. Pick an easy price. No actual price is given, so choose one that makes percents easy: say parking costs $\$100$ before tax.

2. Find the tax and the total. The tax is $27\%$ of $\$100$, which is $\$27$. The customer pays
$$\$100 + \$27 = \$127.$$

3. Write the tax as a fraction of what the customer pays.
$$\frac{27}{127}.$$

4. Turn it into a percent. Divide: $127 \times 0.2 = 25.4$, which leaves $27 - 25.4 = 1.6$, and $1.6 \div 127$ is about $0.0126$. So
$$\frac{27}{127} \approx 0.2126 = 21.26\%.$$

1. Round carefully. The answer choices $21\%$ and $22\%$ are close together, so check which side of $21.5\%$ we are on. $21.5\%$ of $127$ is $127 \times 0.215 = 27.305$, which is more than $27$. So the tax is less than $21.5\%$ of the total, and it rounds to $21\%$.

The answer is $\boxed{\textbf{(A)}\ 21\%}$.

The same dollar amount can be a different percent depending on what you compare it to. Here $\$27$ is $27\%$ of $\$100$ but only about $21\%$ of $\$127$. Whenever a problem moves from "percent of the original" to "percent of the total", write both amounts as actual numbers (using an easy starting value like $100$) and divide.

Use a letter instead of $\$100$. If the price before tax is $p$, the tax is $0.27p$ and the customer pays $p + 0.27p = 1.27p$. The tax share is
$$\frac{0.27p}{1.27p} = \frac{27}{127} \approx 21.3\%,$$
and the $p$ cancels, so the answer is the same for any price.

The other choices come from mixing up the pieces: $27\%$ forgets that the total includes the tax, and $37\%$ is $27 \div 73$, which wrongly treats the price before tax as $100 - 27 = 73$.

Let the price before tax be $100$. The tax is $27$ and the customer pays $127$, so the tax is
$$\frac{27}{127} \approx 0.2126$$
of the total. Since $0.215 \times 127 = 27.305 > 27$, this fraction is below $21.5\%$ and rounds to $21\%$.

The answer is $\boxed{\textbf{(A)}\ 21\%}$.