A taxi charges dollars for the first two miles and cents per quarter mile for every mile after the first two. Which equation describes the cost, in dollars, of a taxi ride of miles?
Question
A taxi charges dollars for the first two miles and cents per quarter mile for every mile after the first two. Which equation describes the cost, in dollars, of a taxi ride of miles?
Solution
Let's denote:
- C as the cost of the taxi ride in dollars
- D as the initial charge for the first two miles in dollars
- c as the additional charge per quarter mile in cents
- m as the total miles of the taxi ride
Since the first two miles are charged at a flat rate D, we only need to consider the cost for the miles after the first two, which is (m - 2) miles.
However, the additional charge is in cents per quarter mile, so we need to convert (m - 2) miles into quarter miles, which is 4(m - 2).
Since 1 dollar is equal to 100 cents, we need to convert the additional charge from cents to dollars by dividing it by 100.
So, the cost C for a taxi ride of m miles can be described by the following equation:
C = D + c/100 * 4(m - 2)
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