Bill and matt are discussing their children. bill tells matt that he has 3 kids, and the product of their ages is 72. he also tells him the sum of the ages of his kids. matt says there is still not enough information to correctly guess the ages of bill's kids. finally, bill says, my youngest child's name is joy. matt can then correctly guess. what are the ages?

This the concept of algebra, the question requires us to find the ages of the three kids. This means we have three variables say x,y and z to represent the 
ages of the kids. From the information given we have been told that the product  of their ages is 72, we haven't been told what their sum is.
Since we have been given 3 variables we need to have at least 3 equations to solve for the variables. From the information we cannot formulate 3 equations because we lack inadequate information.
Therefore we conclude that Matt was right