SOLUTION: George had a bottle filled with juice. He drank 1/5 of the juice in the bottle. An hour later, he drank 2 cups from what was left in the bottle. Two hours later, he drank 1/3 of th

Algebra ->  Systems-of-equations -> SOLUTION: George had a bottle filled with juice. He drank 1/5 of the juice in the bottle. An hour later, he drank 2 cups from what was left in the bottle. Two hours later, he drank 1/3 of th      Log On


   

Question 867108: George had a bottle filled with juice. He drank 1/5 of the juice in the bottle. An hour later, he drank 2 cups from what was left in the bottle. Two hours later, he drank 1/3 of the remaining juice in the bottle. Three hours later, George drank 2 1/2 cups of juice. Before going to bed, he drank 1/2 of what was left. George then measured the amount of juice left and found that there was still 3/4 of a cup of juice in the bottle. How much juice was originally in the bottle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
p = number of cups volume originally in the bottle.

act 1:
p-p%2F5 cups in the bottle

act 2:
p-p%2F5-2 cups in the bottle

act 3:
p-p%2F5-2-%281%2F3%29%28p-p%2F5-2%29

act 4:
p-p%2F5-2-%281%2F3%29%28p-p%2F5-2%29-5%2F2, using 5%2F2=2%261%2F2

act 5:
%281%2F2%29%28p-p%2F5-2-%281%2F3%29%28p-p%2F5-2%29-5%2F2%29

Act 6:
Measurement made of how much juice still in the bottle.
highlight_green%28%281%2F2%29%28p-p%2F5-2-%281%2F3%29%28p-p%2F5-2%29-5%2F2%29=3%2F4%29
Solve for p.