SOLUTION: A water jug with a capacity of 20 gallons is 20 percent full. At the end of every third day, water is added to the jug. If the amount of water added is equal to 50 percent of the w

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A water jug with a capacity of 20 gallons is 20 percent full. At the end of every third day, water is added to the jug. If the amount of water added is equal to 50 percent of the w      Log On


   

Question 1189949: A water jug with a capacity of 20 gallons is 20 percent full. At the end of every third day, water is added to the jug. If the amount of water added is equal to 50 percent of the water in the jug at the beginning of that day, how many days does it take for the jug to be at least 85% full?
A)4 B)4 C)12 D)15 E)20
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


20% of 20 gallons is 4 gallons. So you start with 4 gallons in the jug.

The amount added every third day is half the amount in the jug at the beginning of that day; that means the amount in the jug is multiplied by 1.5. So

4%281.5%29%5Ex=20
1.5%5Ex=5

Use logarithms, or a graphing calculator....

Or...

1.5+=+3%2F2
1.5%5Ex=%283%2F2%29%5Ex

%283%2F2%29%5E4+=+81%2F16+=+5.0625

That is slightly more than what we need; so adding more water to the jug 4 times will fill the jug.

And since water is added to the jug every third day, the number of days it takes to fill the jug is 4*3=12.

ANSWER: C)12