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

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

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

Amount to be charged=d+(n-2)*c/0.25*100
=d+c(n-2)/25
Answer C

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.

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).

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

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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