Question

Dominic is driving on a long road trip. He currently has 10 gallons of gas in his car. Each hour that he drives, his car uses up 1.25 gallons of gas. Write an equation to represent the scenario. How much gas will Dominic have in 3 hours?

Answer 1

(a) Equation:
`T_n = 11.25 - 1.25n`

(b) 7.5 gallons

Explanation:

Given

Current Gas = 10 gallon

Every Hour = -1.25 gallon

Solving for (a): An equation for the scenario

This question represents an Arithmetic Progression and will be solved using the following formula:

`T_n = a + (n - 1)d`

Where

`a = 10`

`d = -1.25`

Substitute these values in the formula

`T_n = 10 + (n - 1) * -1.25`

`T_n = 10 -1.25n +1.25`

Collect Like Terms

`T_n = 10 + 1.25 - 1.25n`

`T_n = 11.25 - 1.25n`

Solving for (b): In this case, n - 3

Substitute 3 for n in
`T_n = 11.25 - 1.25n`

`T_3 = 11.25 - 1.25 * 3`

`T_3 = 11.25 - 3.75`

`T_3 = 7.5`

7.5 gallon of gas left