We need to use the numbers 1, 3, and 5 to fill in the blanks such that the resulting percentage is equal to a fraction with a denominator of 20. That is, we need to find $xy$ and $z$ such that $xy \% = \frac{z}{20}$.

1. Problem Description

We need to use the numbers 1, 3, and 5 to fill in the blanks such that the resulting percentage is equal to a fraction with a denominator of

2

0. That is, we need to find $xy$ and $z$ such that $xy \% = \frac{z}{20}$.

2. Solution Steps

First, we need to remember that percentage means "out of 100". Therefore, $xy \% = \frac{xy}{100}$. So, we are looking for a two-digit number $xy$ and a single-digit number $z$ such that $\frac{xy}{100} = \frac{z}{20}$.

Multiplying both sides by 100, we get

$xy = \frac{100z}{20} = 5z$.

Since we have the numbers 1, 3, and 5, we can make the following two-digit numbers: 13, 15, 31, 35, 51,

5

3. And $z$ must be one of the three numbers.

If $z=1$, $xy=5z=5$. This is not a two-digit number, so $z \neq 1$.

If $z=3$, $xy=5z=15$.

If $z=5$, $xy=5z=25$. We don't have a 2, so $z \neq 5$.

Therefore, $xy=15$ and $z=3$.

The equation becomes $15\% = \frac{3}{20}$. Let us verify this.

$15\% = \frac{15}{100}$. If we divide both numerator and denominator by 5, we get $\frac{15}{100} = \frac{15 \div 5}{100 \div 5} = \frac{3}{20}$.

3. Final Answer

$15 \% = \frac{3}{20}$