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A taxi charges d dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.

Re: A taxi charges d dollars for the first two miles and c cents per quart [#permalink]

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17 Apr 2015, 05:51

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Bunuel wrote:

A taxi charges d dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.

A) dn – c/8(100)

B) cd + 4n-8/200

C) d + (4cn-8c)/100

D) d + 100cn/4

E) 4cd(n-2) – 100

Kudos for a correct solution.

d for 1st 2 miles c cents for every \(\frac{1}{4}\) miles after 2 miles. So 4c for every mile after 2 miles.

This question can be solved conceptually (with Algebra) or by TESTing VALUES.

We're told that a taxi charges D DOLLARS for the first 2 MILES and C CENTS per QUARTER-MILE for every mile after the first 2 miles. Which equation describes cost of a taxi ride of N miles in dollars.

IF.... D = 2 dollars C = 3 cents N = 3 miles

A 3-mile trip would cost 2 dollars (for the first 2 miles) + 3(4) = 12 cents for the 4 additional quarter-miles. Total price (in dollars) = 2.12

Answer A: dn – c/8(100) = (2)(3) - 3/800 = 6 - 3/800 NOT a match

Answer B: cd + 4n-8/200 = (3)(2) + 4(3)/200 = 6 + 12/200 NOT a match

Answer C: d + (4cn-8c)/100 = 2 + (36 - 24)/100 = 2.12 This IS a MATCH

Answer D: d + 100cn/4 = 2 + 900/4 NOT a match

Answer E: 4cd(n-2) – 100 = 24(1) - 100 NOT a match

Re: A taxi charges d dollars for the first two miles and c cents per quart [#permalink]

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19 Apr 2015, 10:26

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A simple way to solve this one is to solve each answer for n=2, meaning the trip is 2 miles long. From the question stem directly, you know the cost should be 'd' dollars when n=2. The only option that satisfies this is C.

A taxi charges d dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.

This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost d is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost d, or subtract the additional cost from d. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).
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Re: A taxi charges d dollars for the first two miles and c cents per quart [#permalink]

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A taxi charges d dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.

A) dn – c/8(100)

B) cd + 4n-8/200

C) d + (4cn-8c)/100

D) d + 100cn/4

E) 4cd(n-2) – 100

Since 1 mile has 4 quarter-miles, a trip of n miles has 4n quarter-miles, and after the first 2 miles that charges d dollars, there are 4n - 8 additional quarter-miles that charge c cents (or c/100 dollars) each. Thus, the total cost in dollars is:

d + (c/100)(4n - 8)

d + (4cn - 8c)/100

Answer: C
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