Answer:
(a) Equation: [tex]T_n = 11.25 - 1.25n[/tex]
(b) 7.5 gallons
Step-by-step 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:
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]a = 10[/tex]
[tex]d = -1.25[/tex]
Substitute these values in the formula
[tex]T_n = 10 + (n - 1) * -1.25[/tex]
[tex]T_n = 10 -1.25n +1.25[/tex]
Collect Like Terms
[tex]T_n = 10 + 1.25 - 1.25n[/tex]
[tex]T_n = 11.25 - 1.25n[/tex]
Solving for (b): In this case, n - 3
Substitute 3 for n in [tex]T_n = 11.25 - 1.25n[/tex]
[tex]T_3 = 11.25 - 1.25 * 3[/tex]
[tex]T_3 = 11.25 - 3.75[/tex]
[tex]T_3 = 7.5[/tex]
7.5 gallon of gas left
