Question

Charlie's gas tank is 1/4 full. After he buys 10 gallons of gas, it is 2/3 full. How many gallons can Charlie's tank hold?

A) 15 gallons

B) 12 gallons

C) 18 gallons

D) 20 gallons

Answer 1

To determine the capacity of Charlie's gas tank, we set up and solved an equation based on the given information. We found that Charlie's gas tank can hold a total of 24 gallons, which doesn't match any of the provided options.

Step-by-step explanation:

Charlie's gas tank is initially 1/4 full and after adding 10 gallons of gas, it is 2/3 full. To find the total capacity of the gas tank, we can set up the equation:

1/4 × total capacity + 10 gallons = 2/3 × total capacity

By solving for the total capacity, we will understand how many gallons Charlie's gas tank can hold. Let's solve the equation step by step:

1. Subtract 1/4 of the total capacity from both sides: 10 gallons = 2/3 × total capacity - 1/4 × total capacity
2. Find the common denominator to combine the fractions: 10 gallons = (2/3 - 1/4) × total capacity
3. Calculate the difference: 10 gallons = (8/12 - 3/12) × total capacity
4. Simplify the fraction: 10 gallons = 5/12 × total capacity
5. Multiply both sides by 12/5 to find the total capacity: total capacity = 10 gallons × 12/5
6. Complete the calculation: total capacity = 24 gallons

Therefore, the total capacity of Charlie's gas tank is 24 gallons. Considering the given options, the closest is option D) 20 gallons, but none of the options are correct.