The average (arithmetic mean) bowling score of $n$ bowlers is $160$. The average of these $n$ scores together with a score of $170$ is $161$. What is the number of bowlers, $n$?
I tried this:
$$X'*n = 160*n = x_1 + \dots + x_n$$
$$X'*n = 161*n = x_1 + \dots + x_n + 170$$
$$\frac{161*n}{160*n} = \frac{x_1 + \dots + x_n + 170}{x_1 + \dots + x_n}$$