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?

Let x = original average score
let y = be the number of students

We need to write two equation using the information given in the scenario in order to work them simultaneously and obtain the results.

let .... (1)
     so x is the original average, so we multiply that average by the amount of     students [y × x] in order to obtain their cumulative score then you add the       nine to that score (because a student got 9 more points) [yx + 9]. Then you    divide that sum by the amount of student in  order to get the new average      which the question says would be 81

...... (2)
   so x is the original average, so we multiply that average by the amount of     students [y × x] in order to obtain their cumulative score then you subtract       three from that score since one student got three less points [yx - 3].  Then     you divide by the number of students (y) and you should 78 like the                 question says.

.... (1)
...... (2)

Now simplify each equation by separating the LHS
..... (1a)
...... (2a)

By subtracting eq (2a) from eq (1a) in order to eliminate x






⇒ y  =  4

Since y = the number of students
then  the number of students = 4