Jose's gas tank is 3/10 full. After 6 gallons of gas it is 4/5 full. How many gallons can Jose's tank hold?
How do I set this up?
Thank you!
You are welcome.
To set up this problem, we can first define a variable to represent the total capacity of Jose's gas tank. Let's call it "x" (in gallons).
We are given that initially, Jose's gas tank is 3/10 full. So we can say that the initial amount of gas in the tank is (3/10) * x.
After adding 6 gallons of gas, the tank becomes 4/5 full. So we can say that the new amount of gas in the tank is (4/5) * x.
Now we can set up an equation to solve for the value of x. Since the initial amount of gas plus 6 gallons should equal the new amount of gas, we can write the equation:
(3/10) * x + 6 = (4/5) * x
To solve this equation, you can follow these steps:
1. Multiply both sides of the equation by 10 to get rid of the denominators:
10 * (3/10) * x + 10 * 6 = 10 * (4/5) * x
Simplifying gives us: 3x + 60 = 8x
2. Subtract 3x from both sides of the equation to isolate the x term on one side:
3x - 3x + 60 = 8x - 3x
Simplifying gives us: 60 = 5x
3. Divide both sides of the equation by 5 to solve for x:
(60) / 5 = (5x) / 5
Simplifying gives us: 12 = x
Therefore, Jose's gas tank can hold 12 gallons.
4/5 - 3/10 = 8/10-3/10 = 5/10 = 1/2
so 6 gallons is half a tank :)