Question

2 clare asks andre to play the following number puzzle:

• pick a number
• add 2
• multiply by 3
• subtract 7
• add your original number

andre’s final result is 27.
which number did he start with?
enter your answer(s) here

Explanation:

Step1: Define the original number

Let the number Andre started with be \( x \).

Step2: Follow the operations

• Pick a number: \( x \)
• Add 2: \( x + 2 \)
• Multiply by 3: \( 3(x + 2) \)
• Subtract 7: \( 3(x + 2) - 7 \)
• Add original number: \( 3(x + 2) - 7 + x \)

Step3: Simplify the expression

\[

$$\begin{align*} 3(x + 2) - 7 + x&= 3x + 6 - 7 + x\\ &= 4x - 1 \end{align*}$$

\]

Step4: Solve for \( x \)

We know the result is 27, so:
\[

$$\begin{align*} 4x - 1 &= 27\\ 4x &= 27 + 1\\ 4x &= 28\\ x &= \frac{28}{4}\\ x &= 7 \end{align*}$$

\]

Answer:

7