a gas tank that is 1/3 full requires 6 gallons to make it 5/6 full.what is the capacity of the tank in gallons.
1/3 x + 6 = 5/6 x
6 = 1/2 x
x = 12
Check:
the 1/3-full tank has 4 gallons. Adding 6 makes 10 gallons, or 5/6 of 12
To solve this problem, we need to first determine the amount of fuel needed to fill 1/6th of the tank. Then, we can find the amount needed to fill the remaining 2/3rd of the tank by multiplying it by 4, as 2/3rd is equivalent to 4/6th.
Let's start by finding the amount of fuel needed to fill 1/6th of the tank. We know that 1/3rd of the tank is already filled, so the amount needed to fill 1/6th of the tank is:
(1/6) * X
where X represents the capacity of the gas tank.
According to the problem statement, this amount is equal to 6 gallons. Therefore, we can write the equation:
(1/6) * X = 6
To find X, we can multiply both sides of the equation by 6 to isolate it:
X = 6 * (6/1)
X = 36
Hence, the capacity of the tank is 36 gallons.