# Problem solving question with average

Johnny had to take a test a day late. His 96 raised the class average from 71 to 72. How many students, including Johnny, took the test?

I tried to do trial and error to see how many students there were but I couldn't figure it out.

Hint: Letting $n$ be the number of students excluding Johnny... $$\text{Old average} = \frac{71n}{n}$$ $$\text{New average} = \frac{71n + 96}{n+1}$$

Note that $\text{New average} - \text{Old average} = 1$.

• I set the equations equal to each other and I got n^2 +25n. So would the number of students be 25? Without Johnny? Because when I plug in 25 for n the equations do not equal eachother
– Ella
Feb 8, 2014 at 22:27
• @Layla The expressions should not be equal, but, rather, they should differ by $1$. Feb 8, 2014 at 22:51
• How do I solve for n if they need to differ by 1?
– Ella
Feb 8, 2014 at 23:03
• @Layla Subtract the old average from the new average and set that equal to $1$. Feb 8, 2014 at 23:17
• By subtracting I get (71n^2 + 96n - 71n^2 - 71n)/ (n(n+1) and I get 25/(n+1)??? So I set that equal to 1 and get 25=n+1? So it's 25 total students?
– Ella
Feb 8, 2014 at 23:21