Question

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. $$6$$ C. $$12$$ D. $$15$$ E. $$20$$

Short answer

The correct answer is option D, which is \(15\) days.

Step-by-step solution

Calculate Initial Water Level

The water jug is initially \(20 \%\) full of its \(20\) gallon capacity. This means there are initially \(20 \%\) of \(20\) gallons = \(20/100 \times 20 = 4\) gallons of water in the jug.

Calculate Water Added Every Third Day

Every third day, water is added to the jug. The amount of water added is \(50 \%\) of the water in the jug at the beginning of that day. So the amount of water in the jug after the third day = \(150 \% = 1.5\) times the amount of water at the beginning of the day.

Calculate Water Level After Each Third Day

Calculate the amount of water in the jug after every third day, by multiplying the existing amount of water by \(1.5\), until it is \(85 \%\) full of its \(20\) gallon capacity.

Continuation of Step 3

Apply the calculation until the jug is at least \(85 \%\) full, that is minimum \(85 \%\) of \(20\) gallons = \(85/100 \times 20 = 17\) gallons.

Count the Days Until Jug Is 85% Full

Count the number of third days it takes until the amount of water in the jug is at least \(17\) gallons.