# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/11

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Putri and Tina's Age

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## Exercise 11

### Question

export const metadata = {
  title: "Putri and Tina's Age",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Putri and Tina are celebrating their birthdays today. Currently, Tina's age is <InlineMath math="2" /> times Putri's age. If in <InlineMath math="6" /> years, Putri's age is <InlineMath math="\frac{2}{3}" /> of Tina's age, what is Putri's current age?


### Choices

- [ ] $$5$$
- [x] $$6$$
- [ ] $$7$$
- [ ] $$8$$
- [ ] $$9$$

### Answer & Explanation

export const metadata = {
  title: "Putri and Tina's Age Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Let Putri's current age be <InlineMath math="x" />, then Tina's age is <InlineMath math="2x" />.

In <InlineMath math="6" /> years:

<MathContainer>
  <BlockMath math="\text{Putri's Age} = x + 6" />
  <BlockMath math="\text{Tina's Age} = 2x + 6" />
</MathContainer>

Given that in <InlineMath math="6" /> years Putri's age will be <InlineMath math="\frac{2}{3}" /> of Tina's age, then:

<MathContainer>
  <BlockMath math="x + 6 = \frac{2}{3}(2x + 6)" />
</MathContainer>

<MathContainer>
  <BlockMath math="3(x + 6) = 2(2x + 6)" />
</MathContainer>

<MathContainer>
  <BlockMath math="3x + 18 = 4x + 12" />
</MathContainer>

<MathContainer>
  <BlockMath math="18 - 12 = 4x - 3x" />
</MathContainer>

<MathContainer>
  <BlockMath math="6 = x" />
</MathContainer>

Thus, Putri's current age is <InlineMath math="6" /> years.


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