# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/12

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 12

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## Exercise 12

### Question

export const metadata = {
  title: "Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

The average mathematics exam score of a class is <InlineMath math="7.5" />. The ratio of male to female students in the class is <InlineMath math="3 : 4" />. If the average score of female students is <InlineMath math="1.75" /> higher than the average score of male students, then the average score of female students is...


### Choices

- [ ] $$6.25$$
- [ ] $$6.50$$
- [ ] $$7.50$$
- [ ] $$7.75$$
- [x] $$8.25$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Let:
- <InlineMath math="\bar{x}_K =" /> Class average score
- <InlineMath math="n_L =" /> Number of male students
- <InlineMath math="n_P =" /> Number of female students
- <InlineMath math="\bar{x}_L =" /> Average score of male students
- <InlineMath math="\bar{x}_P =" /> Average score of female students

Given:
- <InlineMath math="\bar{x}_K = 7.5" />
- <InlineMath math="\frac{n_L}{n_P} = \frac{3}{4} \implies n_L = 0.75 n_P" />
- <InlineMath math="\bar{x}_P = 1.75 + \bar{x}_L" />

The class average score can be obtained as follows:

<BlockMath math="\bar{x}_K = \frac{\bar{x}_P \cdot n_P + \bar{x}_L \cdot n_L}{n_P + n_L}" />

Substitute the known values:

<BlockMath math="\begin{aligned} 7.5 &= \frac{(1.75 + \bar{x}_L)n_P + \bar{x}_L \cdot 0.75n_P}{n_P + 0.75n_P} \\ 7.5 &= \frac{1.75n_P + \bar{x}_L n_P + 0.75\bar{x}_L n_P}{1.75n_P} \\ 7.5 &= \frac{1.75n_P + 1.75\bar{x}_L n_P}{1.75n_P} \\ 7.5 &= \frac{1.75n_P(1 + \bar{x}_L)}{1.75n_P} \\ 7.5 &= 1 + \bar{x}_L \\ \bar{x}_L &= 6.5 \end{aligned}" />

Therefore, the average score of female students is:

<BlockMath math="\bar{x}_P = 1.75 + 6.5 = 8.25" />


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