The problem asks us to select all ratios that are equivalent to the ratio 10:5. The given options are 6:3, 9:2, and 12:1.

1. Problem Description

The problem asks us to select all ratios that are equivalent to the ratio 10:

5. The given options are 6:3, 9:2, and 12:

1.

2. Solution Steps

First, we simplify the ratio 10:5 by dividing both sides by their greatest common divisor, which is

5. $\frac{10}{5} = \frac{10 \div 5}{5 \div 5} = \frac{2}{1}$

So, 10:5 is equivalent to 2:

1.

Now we need to check which of the given ratios are equivalent to 2:

1.

* Check 6:

3. $\frac{6}{3} = \frac{6 \div 3}{3 \div 3} = \frac{2}{1}$. Thus, 6:3 is equivalent to 2:

1.

* Check 9:

2. $\frac{9}{2}$ is not equal to $\frac{2}{1}$. Thus, 9:2 is not equivalent to 2:

1.

* Check 12:

1. $\frac{12}{1}$ is not equal to $\frac{2}{1}$. Thus, 12:1 is not equivalent to 2:

1.

3. Final Answer

The only ratio equivalent to 10:5 is 6:

3.