9514 1404 393
Answer:
3.24
Step-by-step explanation:
The weighted average GPA is ...
(9(2.40) +18g)/(9+18) = 2.96
Then the girls' GPA (g) is ...
((27)(2.96)-9(2.40))/18 = g = 58.32/18 = 3.24
The GPA of the girls in the class is 3.24.
_____
Additional comment
The solution expression can be rearranged to ...
((9+18)(2.96) -(9)(2.40))/18 = g
2.96 +(9/18)(2.96 -2.40) = g
2.96 +(1/2)(0.56) = g
That is, the difference of the boys' GPA from the overall average, multiplied by the ratio of boys to girls, is the amount that must be added to the overall average to get the girls' GPA. This is arithmetic you can do in your head.
The key idea with the average is that the sum of differences from the average is zero. If 9 boys each have a GPA 0.56 units below the average, then twice as many girls will each have a GPA that is half as much above the average.
