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

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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


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[Reveal] Spoiler: OA

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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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New post 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.

d+\(\frac{4c(n-2)}{100}\)
d+\(\frac{4cn-8c}{100}\)

Answer: 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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New post 18 Apr 2015, 11:35
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Hi All,

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

Final Answer:
[Reveal] Spoiler:
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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New post 18 Apr 2015, 13:57
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No of quarter miles in (n-2) miles= \(\frac{(n-2)}{0.25}\)= 4n-8

there total cost for each additional mile past the first 2 miles in dollars = \(\frac{(4n-8)*c}{100}\)

Therefore total cost of the journey = d + \(\frac{(4n-8)*c}{100}\)
=d + \(\frac{(4cn-8c)}{100}\)

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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Given \(d\) dollars for first two miles
\(\frac{4c}{100}\) dollar for every mile

Cost of ride for \(n\) miles \(\,=\,d\,+\,(n-2)*\frac{4c}{100}\)
\(\,=\,d\,+\,\frac{4cn-8c}{100}\)

Answer 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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New post 19 Apr 2015, 04:55
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Amount to be charged=d+(n-2)*c/0.25*100
=d+c(n-2)/25
Answer 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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New post 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.

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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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New post 20 Apr 2015, 04:57
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.


VERITAS PREP OFFICIAL SOLUTION

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

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New post 07 Sep 2017, 16:40
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


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

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New post 07 Sep 2017, 20:47
we have to calculate for n miles.
for first 2 miles , its d$
for remaining (n-2) miles , we calculate as below -

1 quarter mile = c cents
therefore 1 mile = 4c cents

also 100 c = 1 d
hence 1 mile cost = 4c/100 $
for n-2 miles cost = 4c(n-2)/100 $ = (4cn - 8c)/100 $

total cost of n miles in $ = d+ (4cn - 8c)/100

Choice C
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Re: A taxi charges d dollars for the first two miles and c cents per quart   [#permalink] 07 Sep 2017, 20:47
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