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Claire's is twice as tall as Zoe implies that:
[tex]\text{Claire's height = 2x}[/tex]The sum of their ages is 108 inches.
Thus, we have:
[tex]\begin{gathered} x+2x=108 \\ 3x=108 \\ x=\frac{108}{3} \\ x=36 \end{gathered}[/tex]Therefore, Zoe's height is 36 inches while Claire's height is 72 inches