PROBLEM 1-8-1

Before she took her last exam, the average of Tara’s exam scores was 89.  She figures that if she scores 97 on the last exam, her average for all the exams will be 90 and she will get an A for the course.  How many exams, including the last one, are given in the course?

 

SOLUTION 1-8-1

Let n equal the number of exams that Tara has to write.  If she has an average of 89 so far, that implies the easiest way to have an average of 89 is if she has scored 89 on every test so far. Also, we can say that the total of all her marks so far is 89n.  The final total she needs is 90(n+1) in order to get an A.

So,

89n + 97 = 90 (n + 1)

89n + 97 = 90n + 90

90n-89n = 97-90

n = 7

So, she has written 7 tests so far, counting the test she still needs to write, there is a total of 8 tests in the course.