# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/7

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Problem 7

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## Exercise 7

### Question

export const metadata = {
  title: "Problem 7",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Seven years ago, the sum of the ages of the older sibling and the younger sibling was <InlineMath math="26" /> years. Four years from now, twice the age of the older sibling will be equal to twice the age of the younger sibling plus eight years.

The current age of the younger sibling is...


### Choices

- [ ] $$14$$ years
- [ ] $$17$$ years
- [x] $$18$$ years
- [ ] $$20$$ years
- [ ] $$22$$ years

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 7",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Let:
-   <InlineMath math="a =" /> current age of the younger sibling
-   <InlineMath math="k =" /> current age of the older sibling

#### First Condition Analysis

Seven years ago, the sum of the ages of the older sibling and the younger sibling was <InlineMath math="26" /> years.

The mathematical model is:

<MathContainer>
  <BlockMath math="(k - 7) + (a - 7) = 26" />
  <BlockMath math="k + a - 14 = 26" />
  <BlockMath math="k + a = 40 \quad \dots (1)" />
</MathContainer>

#### Second Condition Analysis

Four years from now, twice the age of the older sibling is equal to twice the age of the younger sibling plus eight years.

The mathematical model is:

<MathContainer>
  <BlockMath math="2(k + 4) = 2(a + 4) + 8" />
  <BlockMath math="2k + 8 = 2a + 8 + 8" />
  <BlockMath math="2k - 2a = 8" />
  <BlockMath math="k - a = 4 \quad \dots (2)" />
</MathContainer>

#### Finding the Younger Sibling's Age

We eliminate equation <InlineMath math="(1)" /> and <InlineMath math="(2)" /> to find the value of <InlineMath math="a" />.

<MathContainer>
  <BlockMath math="\begin{aligned} k + a &= 40 \\ k - a &= 4 \\ \hline 2a &= 36 \\ a &= 18 \end{aligned}" />
</MathContainer>

> We subtract the second equation from the first: <InlineMath math="(k+a) - (k-a) = 2a" /> and <InlineMath math="40 - 4 = 36" />.

Thus, the current age of the younger sibling is <InlineMath math="18" /> years.

Therefore, the younger sibling is <InlineMath math="18" /> years old.


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