Question

A class has 9 boys and 21 girls. the class as a whole has a gpa (grade point average) of 2.96, and the boys have a gpa of 2.40. what is the gpa of the girls? (round your answer to two decimal places.)

Answer 1

The gpa of the girls is 3.2

Explanation:

If the whole class of 30 students has a gpa of 2.96 it means that the sum of all the grades divided by 30 is 2.96. This means that the sum of the boy's grades plus the sum of the girl's grades divided by 30 is 2.96

The problem tells us that the boys have a gpa of 2.40 this means that the sum of grades of the boys (SB) divided by 9 is 2.40

`( SB)/(9) = 2.40\\ SB = (2.40(9) = 21.6`

Therefore, the sum of the grades for the boys is 21.6

But as we said before: the sum of the boy's grades (SB) plus the sum of the girl's (SG) grades divided by 30 is 2.96

We're going to write this equation and solve for SG:

`(SB +SG)/(30)=2.96\\(21.6+SG)/(30) =2.96\\ 30(2.96)=21.6 +SG\\88.8=21.6 +SG\\88.8-21.6=SG\\67.2=SG`

Therefore, the sum of the girl's graades is 67.2.

But since we have 21 girls, the gpa for the girls would be:

Girl's GPA = 67.2/21 = 3.2