Question

Tom had to take a taxi to work because his car broke down. The going rate for a taxi in Scranton is a flat rate of $3.00 and $2.95 per mile. Use this information to answer questions 10A - C. 10A.) Write a function C(x) that can be used to represent the situation above for a certain number of miles (x). 10B.) If Tom's trip to work is 17 miles, how much did he have to pay the taxi driver? 10C.) On the way home, Tom asked the taxi driver to make a stop so that he could buy dinner. If his total cost for the taxi ride home was $70.85, how many miles was his trip?

Answer 1

10A) C(x) = 3 + 2.95x

10B) He paid the driver $53.15.

10C) 23 miles

Step-by-step explanation

The rate for the taxi is a flat rate of $3.00 and a rate of $2.95 per mile.

10A) Let x represent the number of miles traveled in the cab.

The cost of taking the taxi will be the sum of the flat rate plus the rate per mile (depending on the number of miles).

This means that the cost (C(x)) is:

C(x) = 3 + 2.95 * x

=> C(x) = 3 + 2.95x

10B) Tom's trip to work is 17 miles.

The amount to pay the driver can be found by replacing x with 17. THis means that the cost is:

C = 3 + (2.95 * 17)

C = 3 + 50.15

C = $53.15

He paid the driver $53.15.

10C) Tom paid a total of $70.85. So, to find the number of miles his trip was, we have to replace Cost, C, with 70.85 and find x:

=> 70.85 = 3 + 2.95x

Collect like terms:

2.95x = 70.85 - 3 = 67.85

x = 67.85 / 2.95

x = 23 miles

His trip was 23 miles.