SOLUTION: Amy has a bucket which contains 4 2/3 gallons of water. She pours out 1/4 of the water. After several pass, 3/7 of the water remaining in the bucket evaporates. How many gallons of

Question 1189933: Amy has a bucket which contains 4 2/3 gallons of water. She pours out 1/4 of the water. After several pass, 3/7 of the water remaining in the bucket evaporates. How many gallons of water remain?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

She pours out 1/4 of the water
3/4 of it remains

If 3/7 of the stuff left behind evaporates, then 4/7 of it is left behind.

(3/4)*(4/7) = 3/7 represents the amount left behind overall (after she pours out the water and after the evaporation).

The mixed number 4 & 2/3 is the same as the improper fraction 14/3
Use the rule
a & b/c = (a*c+b)/c
to convert from a mixed number to improper fraction.

We then multiply that 14/3 by the 3/7 we found to get (14/3)*(3/7) = 2

Answer: 2 gallons of water

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A slightly alternative look:

4 & 2/3 = 14/3
Pouring out 1/4 of that means we lose (1/4)*(14/3) = 7/6 gallons
So we're left with 14/3 - 7/6 = 28/6 - 7/6 = 21/6 = 7/2 gallons

Now to evaporation.
3/7 of that remaining amount (7/2) evaporates, so we lose another (3/7)*(7/2) = 3/2 gallon.

Ultimately we'll have 7/2 - 3/2 = 4/2 = 2 gallons remaining, which matches with the answer above.

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