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URL: https://nakafa.com/en/exercises/high-school/snbt/mathematical-reasoning/try-out/2026/set-1/16

Exercises: Try Out 2026 - Set 1: Real exam simulation to sharpen your skills and build confidence. - Question 16

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## Exercise 16

### Question

export const metadata = {
  title: "Question 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "11/23/2025",
};

Consider the following apple mass table.

| Name | Mass (g) | Mass (g) | Mass (g) | Mass (g) | Mass (g) | Mass (g) |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: |
| Ferdian | <InlineMath math="157" /> | <InlineMath math="163" /> | <InlineMath math="182" /> | <InlineMath math="171" /> | <InlineMath math="167" /> | <InlineMath math="x" /> |
| Belle | <InlineMath math="180" /> | <InlineMath math="175" /> | <InlineMath math="162" /> | <InlineMath math="154" /> | <InlineMath math="161" /> | <InlineMath math="170" /> |

Ferdian and Belle are each collecting <InlineMath math="6" /> apples. The mass of the apples is shown in the table above. The average mass of apples collected by Ferdian is <InlineMath math="3 \text{ grams}" /> greater than the average mass of apples collected by Belle.

The value of <InlineMath math="x" /> is ....


### Choices

- [ ] $$170$$
- [ ] $$175$$
- [x] $$180$$
- [ ] $$185$$
- [ ] $$190$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Question 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "11/23/2025",
};

We will first calculate the average mass of Belle's apples, then use the relationship between Ferdian's and Belle's averages to find the value of <InlineMath math="x" />.

#### Calculating Average Mass of Belle's Apples

The masses of apples collected by Belle are <InlineMath math="180" />, <InlineMath math="175" />, <InlineMath math="162" />, <InlineMath math="154" />, <InlineMath math="161" />, and <InlineMath math="170" />.

<MathContainer>
  <BlockMath math="\bar{x}_{\text{Belle}} = \frac{180 + 175 + 162 + 154 + 161 + 170}{6}" />
  <BlockMath math="\bar{x}_{\text{Belle}} = \frac{1{,}002}{6} = 167" />
</MathContainer>

The average mass of Belle's apples is <InlineMath math="167 \text{ grams }" />.

#### Determining Average Mass of Ferdian's Apples

It is known that Ferdian's average apple mass is <InlineMath math="3 \text{ grams }" /> greater than Belle's.

<MathContainer>
  <BlockMath math="\bar{x}_{\text{Ferdian}} = \bar{x}_{\text{Belle}} + 3" />
  <BlockMath math="\bar{x}_{\text{Ferdian}} = 167 + 3 = 170" />
</MathContainer>

#### Finding the Unknown Value

The masses of apples collected by Ferdian are <InlineMath math="157" />, <InlineMath math="163" />, <InlineMath math="182" />, <InlineMath math="171" />, <InlineMath math="167" />, and <InlineMath math="x" />. Their average is <InlineMath math="170" />.

<MathContainer>
  <BlockMath math="\bar{x}_{\text{Ferdian}} = \frac{157 + 163 + 182 + 171 + 167 + x}{6}" />
  <BlockMath math="170 = \frac{840 + x}{6}" />
</MathContainer>

Multiply both sides by <InlineMath math="6" />:

<MathContainer>
  <BlockMath math="170 \times 6 = 840 + x" />
  <BlockMath math="1{,}020 = 840 + x" />
  <BlockMath math="x = 1{,}020 - 840" />
  <BlockMath math="x = 180" />
</MathContainer>

So, the value of <InlineMath math="x" /> is <InlineMath math="180" />.



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