The problem asks us to select all ratios that are equivalent to the ratio $3:7$. We are given four options: $36:84$, $56:70$, $7:3$, and $5:8$.

1. Problem Description

The problem asks us to select all ratios that are equivalent to the ratio $3:7$. We are given four options: $36:84$, $56:70$, $7:3$, and $5:8$.

2. Solution Steps

To determine if a ratio is equivalent to $3:7$, we can write the ratio as a fraction and simplify it. If the simplified fraction is equal to $\frac{3}{7}$, then the ratios are equivalent.

* Consider the ratio $36:84$. We can write this as the fraction $\frac{36}{84}$. We simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 12:

$\frac{36}{84} = \frac{36 \div 12}{84 \div 12} = \frac{3}{7}$. Therefore, $36:84$ is equivalent to $3:7$.

* Consider the ratio $56:70$. We can write this as the fraction $\frac{56}{70}$. We simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 14:

$\frac{56}{70} = \frac{56 \div 14}{70 \div 14} = \frac{4}{5}$. Since $\frac{4}{5} \neq \frac{3}{7}$, $56:70$ is not equivalent to $3:7$.

* Consider the ratio $7:3$. This is the ratio $3:7$ with the numbers reversed. Therefore, it is not equivalent to $3:7$.

* Consider the ratio $5:8$. This can be written as the fraction $\frac{5}{8}$. Since $\frac{5}{8} \neq \frac{3}{7}$, $5:8$ is not equivalent to $3:7$.

Therefore, only the ratio $36:84$ is equivalent to $3:7$.

3. Final Answer

$36:84$