GMAT Practice Question: For each trip, a taxicab company charges 4.25 dollars for the first mile and 2.65 dollars for...
Question
For each trip, a taxicab company charges 4.25 dollars for the first mile and 2.65 dollars for each additional mile or fraction thereof. If the total charge for a certain trip was 62.55 dollars, how many miles at most was the trip?
- 21
- 22
- 23
- 24
- 25
Topics: linear equations, word problems, inequalities, rates, translations
Solution
Step 1
We first define a variable for the number of additional miles charged.
k = \text{number of additional miles charged}
Step 2
We translate \textbf{\text("the total charge for a certain trip was 62.55 dollars")} and we note that \textbf{\text("sum of")} the first-mile charge and the additional-mile charges equals 62.55.
4.25 + 2.65 \times k = 62.55
Step 3
We isolate the number of additional miles by subtracting the first-mile charge from the total and dividing by the rate per additional mile.
4.25 + 2.65 \times k = 62.55 2.65 \times k = 62.55 - 4.25 = 58.30 k = \frac{58.30}{2.65} = 22
Step 4
We add the initial mile back to find the maximum total miles for the trip.
m = 1 + k = 1 + 22 = 23
Answer
The trip was at most 23 miles, so the answer is \text{Answer C}.
