Question

a bucket of water was ⅓ full, but it still had 2 ¼ gallons of water in it. how much water would be in one fully - filled bucket?

Explanation:

Step1: Convert mixed - number to improper fraction

$2\frac{4}{5}=\frac{2\times5 + 4}{5}=\frac{14}{5}$ gallons.

Step2: Set up an equation

Let the capacity of the full bucket be $x$ gallons. We know that $\frac{1}{3}x=\frac{14}{5}$.

Step3: Solve for $x$

Multiply both sides of the equation by 3: $x = \frac{14}{5}\times3=\frac{42}{5}=8\frac{2}{5}$ gallons.

Answer:

$8\frac{2}{5}$ gallons