Mr. Product

The product of ages of all of Mr. Product's children is 1408. The age of the youngest child is equal to half the age of the oldest child. How many children does Mr. Product have, and how old are they?

Correct answer:

n =  3
a₁ =  8
a₂ =  11
a₃ =  16

Step-by-step explanation:

$$\begin{gathered} 1408=2\times 2\times 2\times 2\times 2\times 2\times 2\times 11=2^7\times 11 \\ 1408=(2\times 2\times 2)\times 11\times (2\times 2\times 2\times 2) \\ {a}_1=2\cdot 2\cdot 2=8 \\ {a}_2=11 \\ {a}_3=2\cdot a_1=2\cdot 8=16 \\ n=3 \\ \text{ Verifying Solution: } \\ s=a_1\cdot a_2\cdot a_3=8\cdot 11\cdot 16=1408 \end{gathered}$$

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