Question

Please solve this 4 the grade algebra problem? 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 will be 81 points. if one of them scored 3 points less, their average score will be 78 points. How many students were in the group?

Answer 1

Let x = the number of students
81x - 9 = 78x + 3
Logic : number of students multiplied by the average will give you total points. You're given the changes (9 more than avg and 3 less than avg). So you subtract 9 from the first avg to get the unchanged avg and add 3 to the second avg to get the unchanged avg. The unchanged avgs should be the same so you set them equal to one another.

Solving for x
81x - 9 - 78x = 78x + 3 - 78x
3x = 12
x = 4