Algebra and Non-Algebra method

The average score of a class is 74.

After adding 1 more student with a score of 100, the average score becomes 75.

Find the no. of students in the class

(Answer = 26 - please solve by non-algebraic method - I have no idea how to explain by non-algebraic method)

Algebra method would be

74x + 100 = 75(x+1)

Thanks

Re: Algebra and Non-Algebra method

Hey Rodimus79.

Hint: Avg1 = Sum_Of_Scores/n = 74. Avg2 = (Sum_Of_Scores + 100)/(n+1) = 75. Eliminate the Sum_Of_Scores variable in one equation to get a function only in terms of n.

Re: Algebra and Non-Algebra method

If by an algebraic method the problem authors meant a method that involves solving equations, then here is a non-algebraic method. If the new student's score were 74, the average score would not change. Instead, 26 extra points were distributed to all students, including the new one, to give each one extra point. Therefore, the new number of students is 26/1 = 26.