Question

A class has 20 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

There are 20+21= 41 people on the class. Let B be the grade points of the boys and G be the grade points of the girls. Since the class has a whole GPA of 2.96, we can write

`(B+G)/(41)=2.96`

On the other hand, the GPA of the boys is

`\begin{gathered} (B)/(20)=2.40 \\ \text{then, the grade points of the boys is} \\ B=20*2.40 \\ B=48 \end{gathered}`

By substituting this result into the first equation, we have

`(48+G)/(41)=2.96`

After multiplying both sides by 41 and subtracting 48 in both sides, we get

`\begin{gathered} 48+G=41*2.96 \\ G=41*2.96-48 \\ \text{then} \\ G=73.36 \end{gathered}`

Since the GPA of the girls is

`(G)/(21)`

we get

`(73.36)/(21)=3.49333`

Hence, by rounding down to the nearest hundredth, the answer is 3.49