Beatrix is twice the height of Violet, and Violet is $\frac{2}{3}$ the height of Georgia. What fraction of Georgia's height is Beatrix's height?
(A) $\frac{9}{7}$
(B) $\frac{2}{3}$
(C) $\frac{4}{3}$
(D) $\frac{5}{4}$
(E) $\frac{3}{2}$
Solution 1

Beatrix is twice the height of Violet who is $\frac{2}{3}$ the height of Georgia.

Therefore, Beatrix is 2 times $\frac{2}{3}$ the height of Georgia, or $\frac{4}{3}$ the height of Georgia.

## Solution 2

Let the heights of Beatrix, Violet and Georgia be represented by $B, V$ and $G$ respectively.

Since Beatrix is twice the height of Violet, then $B=2 V$.

Since Violet is $\frac{2}{3}$ the height of Georgia, then $V=\frac{2}{3} G$.

Substituting $\frac{2}{3} G$ for $V$ in the first equation, we get $B=2 V=2\left(\frac{2}{3} G\right)=\frac{4}{3} G$.

Thus, Beatrix's height is $\frac{4}{3}$ of Georgia's height.

ANSWER: (C)