2009 AMC 10B Problem 5

Work out the left side first, since it is just a number.

1. Twenty percent of $60$ is $12$. Twenty percent less than $60$ is $60 - 12 = 48$.
2. Now we need a number that becomes $48$ when one-third of it is added on.
3. Think of the unknown number as $3$ equal parts. One-third of it is $1$ part. So "one-third more" is $3 + 1 = 4$ parts.
4. Those $4$ parts make $48$, so each part is $12$, and the number (3 parts) is $36$.
5. Check: one-third of $36$ is $12$, and $36 + 12 = 48$. Correct.

The answer is $\boxed{\textbf{(D)}\ 36}$.

"Twenty percent less" and "one-third more" both change a number by a fraction of itself. Here the one-third is a third of the unknown number, not of $48$. Thinking in equal parts ($3$ parts grow to $4$ parts) keeps that straight and avoids the tempting wrong answer $32$.

Twenty percent less than $60$ is $60 \cdot 0.8 = 48$.

If the unknown number is $n$, then one-third more than $n$ is $n + \frac{n}{3} = \frac{4n}{3}$. Setting $\frac{4n}{3} = 48$ gives $n = 48 \cdot \frac34 = 36$.

Check: one-third of $36$ is $12$, and $36 + 12 = 48$.

The answer is $\boxed{\textbf{(D)}\ 36}$.