Question

Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. (Assume the car travels the same distance for each one gallon of gas)

The number of miles traveled varies directly with the number of gallons of gas you use.
a. Write an equation that relates miles traveled to gallons of gas used. (Use any variable you like in the equation.

b. How far can you drive with 3.7 gallons of gas? (Make sure to show the calculations you did to determine this answer)

Answer 1

Explanation:

Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that

1 gallon of gas would be used to drive 392/14 = 28 miles

a) The number of miles traveled varies directly with the number of gallons of gas used.

Let x =number of gallons of gas you use.

Let y = the number of miles travelled.

Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,

y = kx

If 28 miles will require 1 gallon of gas, it means

28 = 1×k

k = 28

So y = 28x

b) we want to determine how far you can drive with 3.7 gallons of gas.

x = 3.7

y = 28x = 28×3.7

y = 103.6 miles