# Thread: arithmetic problem

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 $\frac{12}{11}$ pints.

Set up three columns, showing the number of the pour, and the quantities in each jar after each pour. Like this:
$\begin{array}{c|c|c}
\text{Pour \#} & \text{A} & \text{B}\\
\hline
0 & 2 & 0\\
1 & 1 & 1\\
2 & \frac43 & \frac23\\
3 & 1 & 1\\
4 & \frac65 & \frac45 \\
5 & 1 & 1\\
... & ... & ...\\
9 & 1 & 1\\
10 & \frac{12}{11} & \frac{10}{11}\\
\end{array}$

After each odd-numbered pour, there's a pint in each jar. So after the $10^{th}$ pour, where $\frac{1}{11}$ of the quantity in B gets transferred, there'll be $\frac{12}{11}$ pints in A.