Michael
secondary
student

first question:
The mean of three test grades is 74. What must a fourth grade be to increase the mean to 78?

final question:
The product of two consecutive odd positive integers added to their sum is 119. What are these two integers?

Thanks!

For the mean of the grades of the first three tests to be 74, the SUM of the grades must be 3*74. What must be the sum of the grades of the four tests for a mean of 78? What must be the fourth grade?

The second problem can be solved by checking the first few pairs of odd consecutive integers.

A tougher question would be "The product of two consecutive odd positive integers added to their sum is 1001999. What are these two integers". Then the best recourse would be to express the problem in terms of the even number x that lie between these two odd integers (which would be x-1 and x+1).