Question

A tank holds 800 gallons of water. The gauge indicates that the tank is 3/4 full. Then 100 gallons are drained from the tank to fill a pool 7/8 full. Then 1/3 of a tank of water is added back into the tank. What fraction of the tank is filled with water?

Answer 1

23/24 of the tank is filled with water

Step-by-step explanation

The tank can hold 800 gallons of water and you have 3/4 full:

`800*(3)/(4)=600`

The tank has 600 gallons of water. Then you drain 100 gallons, so now you have 500 gallons of water in the tank.

Then, you add 1/3 of a tank. If one tank can hold 800 gallons, 1/3 of a tank is:

`800*(1)/(3)=266(2)/(3)`

Therefore, you have 266 2/3 plus 500 gallons you had before:

`500+266(2)/(3)=(2300)/(3)`

To find what fraction of the tank that represents we have to divide it by 800:

`(2300)/(3)\colon800=(23)/(24)`

23/24 of the tank is filled with water.