Question

Jane had a bottle filled with juice. At first she drank 1/5 of the juice in the bottle. After 1 hours she drank 1/4 of the juice remaining in the bottle. After another 2 hours she drank 1/3 of the remaining juice in the bottle. At that point Jane checked how much juice was left in the bottle: There was 2/3 of a cup left. No other juice was added to or removed to the bottle. How much juice was in the bottle originally?

Answer 1

X is the size of the bottle. So x/5 + (x/5)/4 + ((x/5)/4)/3 = 2/3 cups

x/5 + x/20 + x/60=2/3; (12x+3x+x)/60=2/3; 16x/60=2/3; (16x)3=(2)(60)
48x=120
x= $\frac{120}{48}$ = 2 $\frac{24}{48}$ = 2 $\frac{1}{2} }$

The bottle is 2 $\frac{1}{2}$ cups