If a taxicab charges x cents for the first 1/9 mile and x/5

We know that the ride is y miles. This also means that the ride is 9y ninths of a mile. The first ninth of a mile is x cents. However, the remaining ride (or 9y - 1 ninths of a mile) cost x/5 cents. So the remainder of the ride costs x/5 * (9y - 1). Putting that together with the first ninth of a mile, the entire ride costs $$x\ +\ \frac{x}{5}\left(9y-1\right)$$ or $$x\ +\frac{9xy-x}{5}$$ So the correct answer is E.