Answer :
Answer:
[tex](225 - 1.5\, x)[/tex].
Step-by-step explanation:
To find the average score of a group, divide the sum of the score of the group members by the number of group members:[tex]\begin{aligned}(\text{group average}) &= \frac{(\text{group total})}{(\text{number of group members})}\end{aligned}[/tex].
Conversely, multiplying the group average by the number of group members would give the total score of the group:
[tex]\begin{aligned}& (\text{group total}) \\ =\; & (\text{group average})\, (\text{number of group members})\end{aligned}[/tex].
In this question, the average of all students (boys and girls), the average of the group of girls, and the number of members in each group are given. To find the group average for the boys, apply the following steps:
- Find the total score of all [tex](10 + 15) = 25[/tex] students.
- Find the total score of the group of girl students.
- Subtract the total score of the group of girl students from the total of all students to find the total score of the group of boy students.
- Divide the total score of the group of boy students by the number of students in the group to find the average.
Given that the average score of all [tex]25[/tex] students is [tex]90[/tex], the total score of these students, combined, would be:
[tex]\begin{aligned}& (\text{total score, boys and girls}) \\ =\; & (\text{group average})\, (\text{number of group members}) \\ =\; & (90)\, (25) \\ =\; & 2250\end{aligned}[/tex].
Similarly, the total score of the girl students would be:
[tex]\begin{aligned}(\text{total score, girls}) &= 15\, x\end{aligned}[/tex].
To find the total score of the boy students, subtract the total score of the girl students from the total score of the class:
[tex]\begin{aligned} & (\text{total score, boys}) \\ =\; & (\text{total score, boys and girls}) - (\text{total score, girls})\\ =\; & 2250 - 15\, x\end{aligned}[/tex].
To find the average score of the boy students, divide the total score of this group ([tex]2250 - 15\, x[/tex]) by the number students in that group ([tex]10[/tex]):
[tex]\begin{aligned}& (\text{group average, boys}) \\ =\; & \frac{(\text{total score, boys})}{(\text{number of group members})} \\ =\; & \frac{2250 - 15\, x}{10} \\ =\; & 225 - 1.5\, x\end{aligned}[/tex].
