Question

5 gallons of diesel weighs 37 pounds. How much does 3 gallons of diesel weigh? Do these quantities (volume and weight) vary directly or inversely? Find the constant of variation.

Answer 1

3 gallons of diesel weighs 22.2 pounds.

The constant of variation is 7.4

The quantities vary directly

Explanation:

37/5=7.4 (constant of variation)

7.4*3=22.2

The quantities vary directly because if the amount of gallons go down, so do the pounds. And direct is if x lowers, so does y.

Answer 2

a) 22.2 pounds

b) The quantities vary directly

c) The constant (k) = 7.4

Explanation:

5 gallons of diesel weighs 37 pounds

1 gallon of diesel will weigh 37/5 = 7.4 pounds

This means 37 = 7.4(5)

To find n gallons, we have 7.4*n

a) 3 gallons weigh 3 *7.4 = 22.2 pounds

b) Recall that for variation,

if x is directly proportional to y

(x α y) , x = ky (k is a constant)

If x is inversely proportional to y,

(x α 1/y) , x = k/y ( k is a constant)

Comparing the options for variation to 37 = 7.4(5), the quantities of weight and volume are directly proportional

c) The constant of the variation = 7.4