The problem asks to select all ratios that are equivalent to the ratio $15:25$. The options are $45:75$, $6:10$, and $9:15$.

1. Problem Description

The problem asks to select all ratios that are equivalent to the ratio $15:25$. The options are $45:75$, $6:10$, and $9:15$.

2. Solution Steps

To find equivalent ratios, we can simplify the given ratio $15:25$ by dividing both numbers by their greatest common divisor (GCD). The GCD of 15 and 25 is

5. $15/5 = 3$ and $25/5 = 5$.

So, the simplified ratio is $3:5$.

Now, we will simplify each of the given ratios and check if they are equivalent to $3:5$.

* Ratio $45:75$

The GCD of 45 and 75 is

1

5. $45/15 = 3$ and $75/15 = 5$.

So, $45:75$ simplifies to $3:5$. Thus, $45:75$ is equivalent to $15:25$.

* Ratio $6:10$

The GCD of 6 and 10 is

2. $6/2 = 3$ and $10/2 = 5$.

So, $6:10$ simplifies to $3:5$. Thus, $6:10$ is equivalent to $15:25$.

* Ratio $9:15$

The GCD of 9 and 15 is

3. $9/3 = 3$ and $15/3 = 5$.

So, $9:15$ simplifies to $3:5$. Thus, $9:15$ is equivalent to $15:25$.

3. Final Answer

All three ratios are equivalent to $15:25$. The ratios are $45:75$, $6:10$, and $9:15$.