How many cups, each with a capacity of 8 fluid ounces, can be filled with water from a cooler that contains 5 gallons of water? (1 gallon = 128 fluid ounces)
The given conversion factors and quantity:
Given rate
$$ \frac{1 \text{ cup }}{8 \text{ fluid ounces }} $$
Given rate
$$ \frac{1\text{ gallon }}{128 \text{ fluid ounces }} $$
Given quantity
$$ 5 \text{ gallons} $$
Since we are asked to find how many cups, we can start with the following and arrange rates and givens accordingly.
$$ \frac{1 \text{ cup }}{8 \text{ fluid ounces }} $$
$$ \frac{1 \text{ cup }}{8 \cancel{\text{ fluid ounces }}} \cdot \frac{128 \cancel{\text{ fluid ounces }}}{1 \cancel{\text{ gallon }}} \cdot 5 \cancel{\text{ gallons}}$$
$$ = \frac{1}{8}\cdot \frac{128}{1} \cdot 5 \text{ cups} $$
$$ = \boxed{80} \text{ cups} $$