# Math

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? By using a strip diagram, 1/5 will be 4/5, 1/4 will be 3/4, and 1/3 will be 2/3. So, will the equation be 2/3x times 3/4x times 4/5x = 2/3. Then, 2/5x = 2/3. 5/2 times 2/5 = 2/3 times 5/2. X is 5/3 of the juice in the bottle

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1. yes

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2. 1 - 1/5 = 5/5 - 1/5 = 4/5 of a bottle remaining.
4/5 - 1/4 = 16/20 - 5/20 = 11/20 of a bottle remaining.
11/20 - 1/3 = 33/60 - 20/60 = 13/60 of a bottle remaining.

Originally, she had X cups of juice in the bottle.
13x/60 = 2/3 cups.
13x = 40,
X = 40/13 = 3 1/13 cups, originally.

Check:
4/5 * 40/13 = 32/13 = 2 6/13 cups remaining.
11/20 * 40/13 = 22/13 = 1 9/13 cups remaining.
13/60 * 40/13 = 40/60 = 2/3 cup remaining.

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