The problem asks to select all ratios that are equivalent to the ratio $3:2$. The options are $15:10$, $8:12$, and $30:20$.

1. Problem Description

The problem asks to select all ratios that are equivalent to the ratio $3:2$. The options are $15:10$, $8:12$, and $30:20$.

2. Solution Steps

To determine if a ratio is equivalent to $3:2$, we can write the ratio as a fraction and simplify it.

If the simplified fraction is equal to $\frac{3}{2}$, then the ratios are equivalent.

First, consider the ratio $15:10$. We can write this as the fraction $\frac{15}{10}$. Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5, we get:

$\frac{15}{10} = \frac{15 \div 5}{10 \div 5} = \frac{3}{2}$

Since $\frac{15}{10} = \frac{3}{2}$, the ratio $15:10$ is equivalent to $3:2$.

Next, consider the ratio $8:12$. We can write this as the fraction $\frac{8}{12}$. Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4, we get:

$\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$

Since $\frac{8}{12} = \frac{2}{3} \neq \frac{3}{2}$, the ratio $8:12$ is not equivalent to $3:2$.

Finally, consider the ratio $30:20$. We can write this as the fraction $\frac{30}{20}$. Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 10, we get:

$\frac{30}{20} = \frac{30 \div 10}{20 \div 10} = \frac{3}{2}$

Since $\frac{30}{20} = \frac{3}{2}$, the ratio $30:20$ is equivalent to $3:2$.

3. Final Answer

The ratios equivalent to $3:2$ are $15:10$ and $30:20$.