9. The two science classes 7A and 7B each consist of a number of boys and a number of girls. Each class has exactly 30 students.
The girls in 7A have a mean score of 48. The overall mean across both classes is 60 .
The mean score across all the girls of both classes is also 60 .
The 5 girls in 7B have a mean score that is double that of the 15 boys in 7A.
The mean score of the boys in 7B is $\mu$. What is the value of $10 \mu$ ?
SOLUTION
672
In 7A there are 15 boys and 15 girls; in 7B there are 25 boys and 5 girls.
All the girls have a total score of $20 \times 60=1200$.
Girls in 7A have a total score of $15 \times 48=720$.
Hence girls in 7B have a total score of $1200-720=480$ and a mean of 96 .
All pupils have a total score of $60 \times 60=3600$.
Hence the 40 boys have a total score of 2400 and a mean of 60 .
The 15 boys in 7A have a mean of $\frac{96}{2}=48$ and total score of 720 .
Hence the 25 boys in 7B have a total score of $2400-720=1680$ and a mean of $\frac{1680}{25}$.
Hence the required number is $\frac{1680}{25} \times 10=672$.