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The tank at a gas station contained 400 gallons of gas. A tanker truck that contained 8,100 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 did the tanker truck put into the station's tank?

Respuesta :

jcherry99

Answer:

1300

Step-by-step explanation:

Let the amount put in the station's tank = x

4(400 + x) = 8100 - x                           Remove the brackets

1600 + 4x = 8100 - x                            Subtract 1600 from both sides

1600 - 1600 + 4x = 8100 - 1600 - x     Do the subtraction

4x = 6500 - x                                        Add x to both sides

4x + x = 6500 - x + x        

5x = 6500                                            Divide by 5

5x/5 = 6500/5                                      

x = 1300

1300 gallons were added to the station's tank.

Answer:

The tanker truck put 1300 gallons of gas into the station's tank.

Step-by-step explanation:

Givens

  • The gas station contained 400 gallons of gas.
  • The truck contained 8,100 gallons of gas.
  • After filling, the truck had 4 times as much gas as the gas station.

In this problem, the unknown variable [tex]x[/tex] represents the amount of gas the truck filled to the gas station. So,

[tex]4(400+x)=8100-x[/tex]

[tex]400+x[/tex] expresses the tank of the gas station filled

[tex]8100-x[/tex] represents the amount of gas is taken out of the truck, which is the same amount that it's being filled to the station.

[tex]4(400+x)[/tex] expresses the comparison between the gas station and the truck, the tank of the truck (after filling) is four times the tanks of the gas station.

Now, we solve for [tex]x[/tex]

[tex]4(400+x)=8100-x\\1600+4x=8100-x\\4x+x=8100-1600\\5x=6500\\x=\frac{6500}{5}=1300[/tex]

Therefore, the tanker truck put 1300 gallons of gas into the station's tank.

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