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A taxi charges d dollars for the first two miles and c cents

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A taxi charges d dollars for the first two miles and c cents

by BTGmoderatorLU » Fri Jun 29, 2018 4:52 pm

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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 miles. Which equation describes the cost of a taxi 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

The OA is C.

Please, can someone assist me with this PS question? I don't have it clear about how can I solve it. Thanks!
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by Vincen » Sat Jun 30, 2018 9:20 am
Hello BTGmoderatorLU.

Let's take a look at your question.

Here is what we know: a taxi charges:

- "d" dollars for the first two miles
- "c" cents per quarter mile for every mile after the first two miles.
- The trip was "n" miles long.

So, the miles after the first two is described by "n-2".

Now, "c" cents per quarter mile means that he charges 4c cents per mile after the first two miles.

Now, if we convert the last expression to dollars we get 4c/100.

So, the total charge for a "n" miles trip is

$$d+\frac{4c(n-2)}{100}=d+\frac{\left(4cn-8c\right)}{100}.$$

Hence, the correct answer is the option C.

I hope it helps. <i class="em em-smiley"></i>
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by Jeff@TargetTestPrep » Wed Jul 25, 2018 4:47 pm
BTGmoderatorLU wrote:A taxi charges d dollars for the first two miles and c cents per quarter mile for every mile after the first two miles. Which equation describes the cost of a taxi 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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Head of GMAT Instruction
[email protected]

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by [email protected] » Thu Jul 26, 2018 11:15 am
Hi All,

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

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

Final Answer: C

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