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 not able to reach the answer through algebra way. Can anyone please help me with that??

Ans - E

cost for first 1/9 mile + cost for remaining miles after first 1/9 mile

x + cost for remaining miles after first 1/9 mile

x + cost per mile * # of remaining miles after first 1/9 mile

x + (x/5 * 9) * (y-1/9)

x + x/5 * (9y-1)

x +(9xy-x)/5

Hey, thanks for the reply buddy.

Let me know if my thought process is right?

I’m assuming the taxi guy takes x cents for the 1st 1/9th part of the mile regardless of the total “y” miles. That’s the reason the equations comes out to be (9y-1) * x/5. or else it would be the conventional one 8y/9 *x/5.

I was actually stuck with this for a solid hr.

Cause if you read the question you would assume that it meant 1/9th part of the “y” miles. Instead, what it meant is 1/9th of just the first mile.

Right, I think we’re on the same page now. The question specifies the price for the first 1/9 mile of the entire trip, then every additional 1/9 mile after that. In order for the question to be instead referring to the first 1/9 mile of every mile, I think the question would need to have the phrase “for every/each mile”.

Consider the case where the question instead asks “what is the charge, in cents, for a ride of z 1/9th miles, where z is a whole number”. I think then you would NOT make the same assumption, even though that section portion of the sentence does not make any statements about how the taxicab splits its charges.

I agree.

The question needs to be presented in an unequivocal manner.