Question

A group of students calculated their average score at a spelling bee. They realized that if one of them scored 9 more points, their average score would be 81 points. If one of them scored 3 points less, their average score would be 78 points. How many students were in the group?

Answer 1

Answer: There are 4 students in the group.

Explanation:

Let the number of students in the group be n

If one of them scored 9 more points , their average score would be 81 points.

So, our equation (1) will be

`(\sum x+9)/(n)=81\\\\\sum x+9=81n`

Similarly,

If one of them scored 3 points less, their average score would be 78 points.

So, our equation (2) will be

`(\sum x-3)/(n)=78\\\\\sum x-3=78n`

So, from equation (1) and (2) we get:

`81n-9=\sum x=78n+3\\\\81n-9=78n+3\\\\81n-78n=3+9\\\\3n=12\\\\n=(12)/(3)\\\\n=4`

Hence, there are 4 students in the group.