An automobile gasoline tank is 3/8 full. After 6 gallons of gasoline (September 2023 - G01)

Correct answer: J. $18.00.
1. Let's represent the tank capacity as a variable.
Let T gallons represent the total capacity of the tank.

2. Find the fraction of the tank that was empty initially.
We know the tank was 3/8 full initially. So, the empty space initially is 1 - (3/8) = 5/8 of the tank.

3. Set up an equation to find the tank capacity.
We can use the information that adding 6 gallons fills the tank from 5/8 empty to 3/4 full.
Empty space after adding 6 gallons = (3/4)T - 6 gallons
We know the empty space initially was 5/8 of the tank: (5/8)T

4. Solve the equation for T.
Since adding the gas fills the remaining empty space:
(5/8)T = (3/4)T - 6
Simplifying the equation:
(1/8)T = 6
T = 48 gallons (This is the tank capacity)

5. Find the empty space when the tank is 3/4 full.
Empty space = (1 - 3/4) * T = (1/4) * 48 gallons = 12 gallons

6. Calculate the cost to fill the tank 3/4 full.
Cost = Empty space when 3/4 full * Price per gallon
Cost = 12 gallons * $1.50/gallon = $18.00