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?

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?

What is the equation? Would the equation be, 2/3 times 3/4 times 4/5x = 2/3? Then 1/2 times 4/5x = 210. Then 4/5x = 210 minus 1/2. Then 4/5x = 209.5 Then 209.5 times 5/4. X= 261.875

I don’t know what I’m doing wrong

Answer 1

(3/4 * 4/5 *2/3 ) x= 2/3 cup

12 x/20 = 1 cup
x = 20/12 = 5/3 = 1.67