Julian and Stacey needed 10 liters of water to fill a tank. Stacey filled the tank with 3 11/12 liters of water. Julian poured 1 2/5 liters less than Stacey into the tank. How much more water is still needed to fill the tank? SHOW YOUR WORK!
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Let x be the amount of water that is still needed to fill the tank. The problem can be equated as 3 11/12 + ( 3 11/12 -1 2/5)+ x = 10 where x is the amount of water that is still needed to fill the tank.
Convert mixed numbers into improper fraction
> 3 11/12 becomes 12*3+11/12= 47/12 and 1 2/5 becomes 5*1 +2/5 = 7/5
> 47/12 + ( 47/12 -7/5)+ x = 10
Subtract both sides by -10
> 47/12 + ( 47/12 -7/5)+ x -10 = 10-10
> 47/12 + ( 47/12 -7/5)+ x -10 = 0
Subtract both sides by -x
> 47/12 + ( 47/12 -7/5)+ x -10 -x= 0 -x
> 47/12 + ( 47/12 -7/5) -10= -x
Multiply both sides by -1
> (-1) 47/12 + (47/12 -7/5) -10 = -x(-1)
> -47/12 - (47/12 -7/5)+ 10 = x
Simplify to find the value of x
> -47/12-151/60+ 10 = x
> -47/12-151/60+ 10 = x
>-193/30+ 10 = x
> 107/30= x or 3 17/30 liters of water is still needed to fill the tank.