Answer
The tank's capacity is $24$ gallons of water.
Work Step by Step
Let us set up an algebraic equation to solve to find how many gallons of water the tank holds.
Let $x$ = the amount of gallons of water the tank holds
Now, we can translate the words into an equation.
The value $18$ is $\frac{3}{4}$ of the capacity of the tank:
$18 = \frac{3}{4}x$
We solve for $x$ by dividing each side of the equation by $\frac{3}{4}$. This means that we multiply each side of the equation by the inverse of $\frac{3}{4}$, which is $\frac{4}{3}$:
$x = \frac{4}{3}(18)$
Multiply to simplify:
$x = \frac{72}{3}$
Divide the numerator by the denominator to simplify the fraction:
$x = 24$
The tank's capacity is $24$ gallons.
