# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/19

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Question 19

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## Exercise 19

### Question

export const metadata = {
  title: "Question 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

The average biology score in a class of <InlineMath math="50" /> students is <InlineMath math="70" />. If the average score of male students is <InlineMath math="76" /> and the number of female students is <InlineMath math="4" /> more than the number of male students, then the average score of female students in the class is...


### Choices

- [ ] $$64$$
- [x] $$64.88$$
- [ ] $$65.09$$
- [ ] $$65.20$$
- [ ] $$65.34$$

### Answer & Explanation

export const metadata = {
  title: "Solution 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

#### Finding the Number of Male and Female Students

It is known that the total number of students is <InlineMath math="50" />.
Let <InlineMath math="n_L" /> be the number of male students and <InlineMath math="n_P" /> be the number of female students.
It is also known that the number of female students is <InlineMath math="4" /> more than the number of male students, so:

<MathContainer>
  <BlockMath math="n_P = n_L + 4" />
</MathContainer>

Since the total number of students is <InlineMath math="50" />, then:

<MathContainer>
  <BlockMath math="\begin{aligned} n_L + n_P &= 50 \\ n_L + (n_L + 4) &= 50 \\ 2n_L + 4 &= 50 \\ 2n_L &= 46 \\ n_L &= 23 \end{aligned}" />
</MathContainer>

So the number of female students is:

<MathContainer>
  <BlockMath math="n_P = 23 + 4 = 27" />
</MathContainer>

#### Calculating Total Scores

Given that the average score of male students (<InlineMath math="\bar{x}_L" />) is <InlineMath math="76" />. Then the total score of male students is:

<MathContainer>
  <BlockMath math="\sum x_L = n_L \times \bar{x}_L = 23 \times 76 = 1748" />
</MathContainer>

Given that the average score of the entire class (<InlineMath math="\bar{x}_{total}" />) is <InlineMath math="70" />. Then the total score of the entire class is:

<MathContainer>
  <BlockMath math="\sum x_{total} = 50 \times 70 = 3500" />
</MathContainer>

#### Calculating the Average Score of Female Students

The total score of female students can be found by subtracting the total score of male students from the total score of the class:

<MathContainer>
  <BlockMath math="\sum x_P = 3500 - 1748 = 1752" />
</MathContainer>

Thus, the average score of female students (<InlineMath math="\bar{x}_P" />) is:

<MathContainer>
  <BlockMath math="\bar{x}_P = \frac{\sum x_P}{n_P} = \frac{1752}{27} \approx 64.88" />
</MathContainer>

So, the average score of female students is <InlineMath math="64.88" />.


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