1. ## arithmetic problem

I have two one-quart jars; the first is filled with water, and the second is empty. I pour half of the water in the first jar into the second, then a third of the water in the second jar into the first, then a fourth of the water in the first jar into the second, then a fifth of the water in the second jar into the first, and so on. How much water is in the first jar after the 10th pour? Express your answer as a common fraction.

2. Hello sri340
Originally Posted by sri340
I have two one-quart jars; the first is filled with water, and the second is empty. I pour half of the water in the first jar into the second, then a third of the water in the second jar into the first, then a fourth of the water in the first jar into the second, then a fifth of the water in the second jar into the first, and so on. How much water is in the first jar after the 10th pour? Express your answer as a common fraction.
I think it's just $\displaystyle \frac{12}{11}$ pints.

Set up three columns, showing the number of the pour, and the quantities in each jar after each pour. Like this:
$\displaystyle \begin{array}{c|c|c} \text{Pour \#} & \text{A} & \text{B}\\ \hline 0 & 2 & 0\\ 1 & 1 & 1\\ 2 & \frac43 & \frac23\\ 3 & 1 & 1\\ 4 & \frac65 & \frac45 \\ 5 & 1 & 1\\ ... & ... & ...\\ 9 & 1 & 1\\ 10 & \frac{12}{11} & \frac{10}{11}\\ \end{array}$
After each odd-numbered pour, there's a pint in each jar. So after the $\displaystyle 10^{th}$ pour, where $\displaystyle \frac{1}{11}$ of the quantity in B gets transferred, there'll be $\displaystyle \frac{12}{11}$ pints in A.