The problem asks to identify which of the given ratios are equivalent to the ratio $5:30$. The given ratios are $15:90$, $1:6$, $7:32$, $6:31$, and $3:28$.

1. Problem Description

The problem asks to identify which of the given ratios are equivalent to the ratio $5:30$. The given ratios are $15:90$, $1:6$, $7:32$, $6:31$, and $3:28$.

2. Solution Steps

First, we simplify the given ratio $5:30$ by dividing both sides by their greatest common divisor, which is

5. $5:30 = \frac{5}{5} : \frac{30}{5} = 1:6$.

Now we check each of the given ratios:

* $15:90$: We simplify this ratio by dividing both sides by their greatest common divisor, which is

1

5. $15:90 = \frac{15}{15} : \frac{90}{15} = 1:6$.

So $15:90$ is equivalent to $5:30$.

* $1:6$: This is the same as the simplified ratio of $5:30$.

So $1:6$ is equivalent to $5:30$.

* $7:32$: This ratio is not equal to $1:6$.

So $7:32$ is not equivalent to $5:30$.

* $6:31$: This ratio is not equal to $1:6$.

So $6:31$ is not equivalent to $5:30$.

* $3:28$: This ratio is not equal to $1:6$.

So $3:28$ is not equivalent to $5:30$.

Therefore, the ratios equivalent to $5:30$ are $15:90$ and $1:6$.

3. Final Answer

The ratios equivalent to $5:30$ are $15:90$ and $1:6$.