Lara's sequence

Lara starts with a number less than 20. She divides it by 2 and adds 6. She then divides this result by 3. Her answer is 4.5. What number does she start with?

Final Answer:

x =  15

Step-by-step explanation:

$$\begin{gathered} x_2/3=4.5 \\ {x}_2=3\cdot 4.5=13.5 \\ x/2+6=x_2 \\ x/2=x_2-6 \\ x=2\cdot (x_2-6)=2\cdot (13.5-6)=15 \\ \text{ Verifying Solution: } \\ {X}_1=x/2+6=15/2+6=\frac{27}{2}=13\frac{1}{2}=13.5 \\ {X}_2=X_1/3=13.5/3=\frac{9}{2}=4\frac{1}{2}=4.5 \end{gathered}$$

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