We are looking for the capacity of the container so let x represent how many gallons the container will hold.
When the container is 1/10 full it will have ( 1/10) times x gallons in it. To see that this is correct, lets think of a container that holds 100 gallons. If it were one tenth of the way full, it would have 10 gallons in it or (1/10) times 100. Since we don’t know the capacity of the container in this problem, we represent that by x and the number of gallons when it is 1/10 full by 1/10 times x.
Using that same reasoning, it will have 3/5 times x gallons in it when it is three fifths of the way full.
To get the equation we reason that we have a container that is 1/10 of the way full,
and we are going to add 13 gallons to it.
We know once we add the 13 gallons the container will be 3/5 full.
So
Using the picture to write and equation gives us
To solve the equation, multiply both sides by 10 to get
x + 130 = 6x
Subtract x from both sides to get
130 = 5x
Divide both sides by 5 to get x = 26.
So the capacity of the tank is 26 gallons.