In order to solve problems involving averages, you should be able to:
An average problem in algebra usually involves finding the grade a person needs to make a certain grade in a class. Anytime you know a teacher’s grading system, you can determine your average and find out what kind of grade is needed to make an “A” or a “B”.
Suppose Kirk has taken three tests and made 88, 90, and 84. Kirk’s teacher tells the class that each test counts the same amount. Kirk wants to know what he needs to make on the fourth test to have an overall average of 90 so he can make an A in the class.
The key here is that all the tests count the same. So this is a case where we need to add all four test grades and divide by four. The only problem is, we don’t know the fourth test grade; that’s what we want to find out. So if we call the fourth test grade x, we can add up the four grades and divide by 4. This gives the average of the four test grades. Since we want that average to be 90, we set up the equation
Now we solve the one-variable equation
to find the value of x.
We have determined that Kirk needs to make a 98 on the fourth test to get an A. If we check this answer, we get: