The problem asks us to find the number that makes the ratio $72:x$ equivalent to the ratio $12:3$.

1. Problem Description

The problem asks us to find the number that makes the ratio $72:x$ equivalent to the ratio $12:3$.

2. Solution Steps

We are given that the ratio $72:x$ is equivalent to $12:3$. This means that $\frac{72}{x} = \frac{12}{3}$.

We can solve for $x$ by cross-multiplying.

$12x = 72 \times 3$

$12x = 216$

$x = \frac{216}{12}$

$x = 18$

Alternatively, we can find the scale factor.

We want to find $x$ such that $\frac{72}{x} = \frac{12}{3}$.

We can see that $72 = 12 \times 6$.

Therefore, we have

$\frac{12 \times 6}{x} = \frac{12}{3}$

We can divide both the numerator and denominator of the left side by 12:

$\frac{6}{\frac{x}{12}} = \frac{1}{3}$

So $\frac{x}{12} = 6 \times 3 = 18$

So $x = 12 \times \frac{3}{1} = 36$.

We have that $12:3$ is equivalent to $72:x$. Then $\frac{12}{3} = \frac{72}{x}$.

We can simplify $\frac{12}{3} = 4$.

Then $4 = \frac{72}{x}$.

Multiplying both sides by $x$ gives $4x = 72$.

Dividing both sides by 4 gives $x = \frac{72}{4} = 18$.

3. Final Answer

$18$