Question Find the weight-to-volume ratio of water. Given that 50 gallons of water weigh 417 pounds, express the relationship between the volume $v$ (in gallons) and weight $w$ (in pounds) as an equation.

Studdy Solution
Express the equation in terms of a fraction and then as a decimal.
As a fraction: $$w = \frac{417}{50} \cdot v$$
As a decimal: $$w = 8.34 \cdot v$$
Include proper units: $$w \text{ (pounds)} = 8.34 \text{ (pounds per gallon)} \cdot v \text{ (gallons)}$$
(a) The ratio of the weight of water to its volume as a unit rate is $8.34$ pounds per gallon. (b) The equation that relates $v$ and $w$ is $w = 8.34 \cdot v$.