i’m not so sure if i can do this problem.

Question

George’s car has a 20 gallon gas tank. travel 22 miles per gallon. If M is the number of miles driven since the last fill up, he can use this formula to find out how much gas is left in the gas tank: G = 20 - (1/22) M

why does the value 22 appear in the denominator of the fraction?

why does a computation “start” with the value 20?

if George has driven 100 miles since you filled the tank, how much gas is left in the tank?

after filling up the tank, how far can George drive and be left with 4 gallons in the tank?

The “low fuel” light comes on when there is 1 gallon left. How far can George drive after a fill up before “the low fuel” light comes on?

Answer 1

Initially, at M = 0 miles traveled, the volume of gas in the full tank was G = 20 gallons. The same result can be obtained by substituting M = 0 into the formula G = 20 - M/22. This is why the computation “starts” with the value 20.

Next consider these quantities after traveling d = 22 miles. In this case, 1 gallon of gas is used, and the remaining volume should be 20 - 1 = 19 gallons. Indeed, from the formula we obtain G = 20 - 22/22 = 19. Thus, the value 22 appears in the denominator of the fraction because we can ride M = 22 miles per gallon of gas, and the consumption is M/22 gallons of gas per M miles traveled.

If George has driven 100 miles since the tank was filled, there is still G = 20 - 100/22 = 15.45454546 gallons left (we just have to substitute M = 100 into the formula for remaining gas volume G).

When 4 gallons left in the tank, G = 4, and from our formula we have 4 = 20 - M/22, which we have to solve for the number of traveled miles M, giving M = 352 miles. This is how far George can drive and be left with 4 gallons in the tank.

For the case of 1 gallon left, we repeat the same calculations with G = 1, i.e., 1 = 20 - M/22, giving M = 418 miles traveled before the “low fuel” light comes on.

Answer 2

why does the value 22 appear in the denominator of the fraction?

Because the unit for 22 is miles/gallon, when it is 1/22, the unit of miles will cancel with the unit of M (miles), so that the unit of the term is gallons

why does a computation “start” with the value 20?

Because that is the initial and the total amount of the gas in the gas tank

if George has driven 100 miles since you filled the tank, how much gas is left in the tank?

Let M be 100, you'll get G = 20 - (1/22)(100), that will be your G value

after filling up the tank, how far can George drive and be left with 4 gallons in the tank?

Let G be 4, find your M

The “low fuel” light comes on when there is 1 gallon left. How far can George drive after a fill up before “the low fuel” light comes on?

Let G be 1, find your M