The problem asks us to select all ratios equivalent to $3:7$ from a given set of ratios. The given options are $36:84$, $56:70$, $7:3$, and $5:8$.

1. Problem Description

The problem asks us to select all ratios equivalent to $3:7$ from a given set of ratios. The given options are $36:84$, $56:70$, $7:3$, and $5:8$.

2. Solution Steps

We need to determine which of the given ratios are equivalent to $3:7$. To do this, we can simplify the given ratios and compare them to $3:7$.

* Consider the ratio $36:84$. We can simplify this by dividing both numbers by their greatest common divisor, which is

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2. $36 \div 12 = 3$

$84 \div 12 = 7$

So, $36:84 = 3:7$. This ratio is equivalent to $3:7$.

* Consider the ratio $56:70$. We can simplify this by dividing both numbers by their greatest common divisor, which is

1

4. $56 \div 14 = 4$

$70 \div 14 = 5$

So, $56:70 = 4:5$. This ratio is not equivalent to $3:7$.

* Consider the ratio $7:3$. This ratio is simply the inverse of $3:7$, and is therefore not equivalent to $3:7$.

* Consider the ratio $5:8$. There is no obvious common factor, and it's clear that this is not equivalent to $3:7$.

3. Final Answer

The only ratio equivalent to $3:7$ is $36:84$.