WAEC Further Mathematics 2017 Paper

Concept:The overall class average is the weighted mean of the boys' and girls' average scores.We use the total sum of scores to isolate the boys' average in terms of $x$.Explanation:Total number of students is $10 + 15 = 25$.Given overall average is $90$, so the total sum of all scores is:$$25 \times 90 = 2250$$Let the total score of girls be $S_g$. Since the girls' average is $x$,$$\frac{S_g}{15} = x \Rightarrow S_g = 15x$$Therefore, total score of boys, $S_b$, is:$$S_b = 2250 - 15x$$There are 10 boys, so the boys' average score is:$$\frac{S_b}{10} = \frac{2250 - 15x}{10}$$Simplifying:$$\frac{2250}{10} - \frac{15x}{10} = 225 - \frac{3x}{2}$$This matches option B.Answer:$$\boxed{225 - \frac{3x}{2}} \quad \text{(Option B)}$$