Math Snap

STEP 1

1. We are given a ratio $72:24$.
2. We need to find a number $x$ such that the ratio $x:2$ is equivalent to $72:24$.
3. Ratios are equivalent if their cross-products are equal.

STEP 2

1. Simplify the given ratio.
2. Set up an equation for equivalent ratios.
3. Solve for the unknown number.

STEP 3

Simplify the given ratio $72:24$.
Divide both terms of the ratio by their greatest common divisor, which is $24$.
$$\frac{72}{24} : \frac{24}{24} = 3:1$$

STEP 4

Set up an equation for equivalent ratios.
We want $x:2$ to be equivalent to $3:1$.
$$\frac{x}{2} = \frac{3}{1}$$

Solve for $x$.
Multiply both sides by $2$ to isolate $x$.
$$x = 3 \times 2$$ $$x = 6$$ The number that makes the ratio equivalent to $72:24$ is:
$$\boxed{6}$$