Question

The weight of water in a trough is directly proportional to the quantity of water in the trough. If 20 gallons of water weigh 166 pounds, what is the weight of 30 gallons of water? Find the constant of proportionality in pounds per gallon. Then write an equation for the relationship using p for pounds and g for gallons. Start the equation p =.

Answer 1

The equation for direct variation is

p = k*q

where k is the constant of proportionality

Putting in what we know

166 lbs = k * 20 gallons

Divide each side by 20 gallons

166 lbs / 20 gallons = k

8.3 lbs per gallon = k

The constant of proportionality is 8.3 pounds per gallon

We have 30 gallons

p = 8.3 lbs/ gal * 30 gal

p =249 pounds

When we have 30 gallons, it will weight 249 pounds

p = 8.3 lbs/gallon * g