Final answer:
Trey's gas tank has a total capacity of 24 gallons, calculated using fractions and algebra with given information about how much the volume changed after adding gas.
Step-by-step explanation:
The student's question involves a real-world application of fractions and algebra to figure out the total capacity of a gas tank. Here's how to determine how many gallons Trey's tank can hold.
Step-by-Step Explanation
Let the total capacity of the tank be x gallons.
Since the tank was 1/4 full, it contained x/4 gallons of gas initially.
After adding 10 gallons, the tank becomes 2/3 full, so it now contains (2/3)x gallons.
Form the equation based on the information given: x/4 + 10 = (2/3)x.
Multiply all terms by 12 to clear the fractions: 3x + 120 = 8x.
Rearrange the equation to solve for x: 120 = 5x.
Divide by 5 to find x: x = 24.
Trey's gas tank can hold 24 gallons when full.