Gas tank word problem

The tank at a gas station contained 400 gallons of gas. A tanker truck that contained 8100 gallons of gas filled the station's tank. After that the tanker truck had 4 times as much gas as the station's tank. How much gas did the tanker truck put into the station's tank?

Solution

Let x be the amount of gas in gallons that was put in the tank at the gas station to fill it up.

The tank now has 400 + x when it is full

The amount of x gallons given to the tank at the gas station was removed from the tanker.

The tanker truck now has 8100 – x

The tanker truck now has 4 times as much gas as the station's tank

8100 – x is 4 times as big as 400 + x

8100 – x = 4 (400 + x)

8100 – x = 1600 + 4x

8100 – x + x = 1600 + 4x + x

8100 = 1600 + 5x

8100 – 1600 = 1600 – 1600 + 5x

8100 – 1600 = 5x

6500 = 5x

x = 1300

1300 gallons of gas was added to the tank to fill it up