Final answer:
To determine the total capacity of Dante's gas tank, we set up an equation based on the given information. Through solving the equation, we find that Dante's gas tank can hold 27 gallons of gas when full.
Step-by-step explanation:
The student is asking how many gallons Dante's gas tank can hold. Initially, Dante's tank is 1/2 full, and after adding 9 gallons of gas, it is 5/6 full. We can set up an equation to solve for the total capacity of the gas tank.
Let the total capacity of the tank be x gallons. So, when the tank is 1/2 full, it contains x/2 gallons of gas. After adding 9 gallons, the amount of gas in the tank is x/2 + 9 gallons. We are given that after adding 9 gallons, the tank is 5/6 full, which is equivalent to 5x/6 gallons.
Thus, we can write the equation as follows:
x/2 + 9 = 5x/6
Solving this equation:
Multiply through by 6 to eliminate the fractions: 3x + 54 = 5x
Subtract 3x from both sides: 54 = 2x
Divide by 2 to find x: x = 27
Therefore, Dante's gas tank can hold a total of 27 gallons when full.