SOLUTION: A tank holds 800 gallons of water. The gauge indicates that the tank is ¾ full; then 100 gallons are drained from the tank to fill a pool 7/8 full. Next, 1/3 of a tank of water i
Question 222976: A tank holds 800 gallons of water. The gauge indicates that the tank is ¾ full; then 100 gallons are drained from the tank to fill a pool 7/8 full. Next, 1/3 of a tank of water is added back in. What fraction of the tank is filled with water?
I have figured out that 800 gallons = 3/4 full (tank) and that 3/4 = 6/8. I do not know how to solve the problem from here! Found 2 solutions by Theo, stanbon:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! A tank holds 800 gallons of water. The gauge indicates that the tank is ¾ full; then 100 gallons are drained from the tank to fill a pool 7/8 full. Next, 1/3 of a tank of water is added back in. What fraction of the tank is filled with water?
Let T represent a full tank = 800 gallons of water.
Let P represent a full pool = ???
3/4 * T - 100 = 7/8 * P
This formula says that three quarters of the tank minus 100 gallons equals 7/8 of the capacity of the pool.
You are adding 1/3 of a tank of water back in to the tank ?????
This problem apparently doesn't have anything to do with the pool.
Here's why I think that way.
Your tank is 3/4 full meaning it have 800*3/4 = 600 gallons in it.
you drain 100 gallons from it so you are left with 500 gallons in the tank.
you add 1/3 of a tank full of water back into it, so you are adding 800/3 = 266 and 2/3 gallons into it.
500 + 266 and 2/3 = 766 and 2/3 gallons / 800 = .9583333333 percent full.
in fractions, you would have (2300/3) / (2400/3) which is the same as 2300/2400.
2300/2400 is the same as 23/24 = .95833333333 so your fraction of the tank that is full would be 23/24.
The pool had nothing to do with it other than to add extraneous information as far as I could see.
You can put this solution on YOUR website! A tank holds 800 gallons of water.
The gauge indicates that the tank is ¾ full = 600 gallons
; then 100 gallons are drained from the tank = 500
to fill a pool 7/8 full.
Next, 1/3 of a tank of water is added back in = 500 + (1/3)800 = 766 2/3 gallons
--------
What fraction of the tank is filled with water?
-----
Fraction = (766 2/3)/800 = [2300/3]/800 = 2300/2400 = 23/24
==================================================================
Cheers,
Stan H.
(