Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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:

$$X'*n = 160*n = x_1 + \dots + x_n$$

$$X'*n = 161*n = x_1 + \dots + x_n + 170$$

$$\frac{161*n}{160*n} = \frac{x_1 + \dots + x_n + 170}{x_1 + \dots + x_n}$$

share|cite|improve this question
@Belgi, I have edited the original post. – guru Oct 6 '12 at 2:52
While writing down an equation is a good way to solve the problem, one can do it in an algebra-free way. Suppose that the new bowler had bowled $160$. Then the average wouldn't change. But she bowled $170$, which gave everybody, including herself, $1$ extra point on average. Thus, including the new bowler, there must be $10$ people. – André Nicolas Oct 6 '12 at 2:52
up vote 0 down vote accepted

Assume the total score of the $n$ bowlers is $S$, then the average is

$$A = \frac{S}{n} = 160\,,\quad (1) $$

The second statement is telling you that the average of these $n$ scores adding to them the score (170) of another player (you will have $n+1$ bowlers) is 161. That translates to

$$ 161 = \frac{ S+170 }{n+1}\,,\quad (2) \,. $$

Now, solve the two equations to get $n$. Solution $(n=9)$

share|cite|improve this answer

Hint: what is the total score of the original $n$ bowlers? If you add another bowler who hits $170$, what is the total? How many bowlers are there now?

share|cite|improve this answer
I can't understand. – guru Oct 6 '12 at 2:59
The definition of the average score is the total score divided by the number of bowlers. – Ross Millikan Oct 6 '12 at 3:01
I know what average is. – guru Oct 6 '12 at 3:02
@guru: Then what don't you understand? The total score is $160n$. Having done that, try the next two. – Ross Millikan Oct 6 '12 at 3:05
What i did is correct? See the original post again please. – guru Oct 6 '12 at 3:32

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.