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

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

by BTGmoderatorAT » Fri Feb 23, 2018 4:01 am

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If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number?

A. x + (xy - x)/45
B. x - (xy - x)/45
C. (2x + 9y)/5
D. x + (9x - y)/5
E. x + (9xy - x)/5

I'm confused how to set up the formulas here. Can any experts help?

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Source: Beat The GMAT — Problem Solving | Fri Feb 23, 2018 4:01 am

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by ErikaPrepScholar » Fri Feb 23, 2018 10:12 am

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.