1a. The number of miles that this car has traveled if it has the following amount of gas left in the tank are;
15 gallons ↔ 30 miles.
10 gallons ↔ 180 miles.
2.5 gallons ↔ 405 miles.
1b. An equation that represents the relationship between that distance the car has traveled in mile (d) and the amount of gas left in the tank in gallons (x) is d = 480 - 30x.
1c. At 90 miles, the amount of gas left in the tank is 13 gallons.
At 246 miles, the amount of gas left in the tank is 7.8 gallons.
1d. An equation that can be used to find the amount of gas left in the tank (x), if we know the car has traveled d miles is x = 16 - d/30.
Since this car has a 16-gallon fuel tank and it has a gasmileage of 30 miles per gallon when driven on a highway, the number of miles that this car has traveled if it has the following amount of gas left in the tank can be calculated as follows;
Gas left (15 gallons) = 30 × (16 - 15)
Gas left (15 gallons) = 30 miles.
At 10 gallons, we have;
Gas left (10 gallons) = 30 × (16 - 10)
Gas left (10 gallons) = 180 miles.
At 2.5 gallons, we have;
Gas left (2.5 gallons) = 30 × (16 - 2.5)
Gas left (2.5 gallons) = 405 miles.
Part 1b.
An equation that represents the relationship between that distance the car has traveled in mile (d) and the amount of gas left in the tank in gallons (x) can be written as follows;
d = 30 × (16 - x)
d = 480 - 30x.
Part 1c.
When the car has traveled 90 miles, the amount of gas left in the tank in gallons (x) is given by;
90 = 480 - 30x
30x = 390
x = 13 gallons.
When d is 246 miles, the x-value is given by;
246 = 480 - 30x
30x = 234
x = 7.8 gallons.
Part 1d.
An equation that can be used to find the amount of gas left in the tank (x), if we know the car has traveled d miles can be written as follows;
d = 30(16 - x)
d/30 = 16 - x
x = 16 - d/30