Justin's gas tank is 1/4 full. After he buys 9 gallons of gas, it is 5/8 full. How many gallons can Justin's tank hold?
How would i set that up?
5/8 = 1/4 = 5/8 - 2/8 = 3/8
3/8x = 9
x = ?
To set up the problem, we can use the information provided and represent it algebraically. Let's denote the capacity of Justin's gas tank as "x" (in gallons).
Given:
- Justin's gas tank is initially 1/4 full.
- After buying 9 gallons of gas, the tank is 5/8 full.
Let's write these statements as equations:
1. Initially, the tank is 1/4 full:
The amount of gas in the tank = 1/4 of the tank's capacity (x):
(x/4)
2. After buying 9 gallons of gas, the tank is 5/8 full:
The amount of gas in the tank = 5/8 of the tank's capacity (x):
(x * 5/8)
Now, we can equate these two expressions since they represent the same amount of gas in the tank:
(x/4) = (x * 5/8)
Now, we can solve this equation to find the capacity of Justin's gas tank (x).
To set up the problem, let's denote the maximum capacity of Justin's gas tank as 'x' gallons.
Since Justin's gas tank was initially 1/4 full, we can represent this as (1/4)*x gallons.
After Justin buys 9 gallons of gas, the tank is now 5/8 full, which can be represented as (5/8)*x gallons.
Now, we can set up an equation using this information:
(1/4)*x + 9 = (5/8)*x
To solve for 'x', we can follow these steps:
1. Multiply both sides of the equation by the common denominator of 8 to eliminate the fractions:
8 * (1/4)*x + 8 * 9 = 8 * (5/8)*x
2x + 72 = 5x
2. Simplify the equation by subtracting '2x' from both sides:
2x - 2x + 72 = 5x - 2x
72 = 3x
3. Divide both sides of the equation by 3 to isolate 'x':
72/3 = (3x)/3
24 = x
So, Justin's gas tank can hold a maximum of 24 gallons.