I need help with a algebra problem

Question

George rides a cab three days a week. He pays $3.50 for the cab to pick him up. He pays an additional fee for each mile driven. In one week, George paid 35.25. If he rides 11 miles each day, how much does he pay per mile?

Answer 1

Hi Marisol,

Let k = the cost per mile that the cab drives

Let t = the number of times George takes a cab per week

So the total cost that George pays to ride the cab in a week will be...

Total Cost = K * (Total number of miles the cab drives) + T * (Total number of times George rides a cab)

We're told the following:

1. Total Cost for a week is $35.25
2. Total times George rides a cab is 3 times
3. Total miles George rides is 11 miles per day (at 3 rides for the week) is 33 miles total
4. Each pick up T, is $3.50

Total Cost = K * (Total number of miles the cab drives) + T * (Total number of times George rides a cab)

35.25 = K * 33 + 3.50 * 3

35.25 = 33K + 10.50

24.75 = 33K

K = 24.75 / 33

= $0.75

Rate is $0.75 per mile driven

Answer 2

The total he pays in the week for the cab to just come to get him is $3.50 • 3 or $10.50. Since he paid $35.25 total for the week, we could subtract $10.50 from that to find out how much money he is spending for the miles. So $35.25 - $10.50 = $24.75. Since he went a total of 11 • 3 or 33 miles, then he paid $24.75/33 miles = $0.75 per mile.

Answer 3

George paid a flat fee of $3.50 for each ride + an additional rate (rate) times the # of miles driven in a week and pays a total of $35.25 (total) in a week

The formula would look like

total in a week ($) = flat fee($) X # of rides + rate ($/miles) X miles

He had 3 rides in a week, therefore # of rides = 3

He rides 11 miles each day, and 3 rides in a week. Therefore miles in a week = 3 x 11 miles = 33 miles

total in a week = $35.25, let's put it all together and solve for rate

$35.25 = $3.50 X 3 + rate X 33 miles

Now solve for rate

$35.25 - $10.50 = $10.50 + rate X 33 - $10.50

$24.75 = rate X 33

$24.75/ 33 = rate X 33 / 33

rate = $0.75 / mile

Plug the answer back into the original equation to check your answer

$35.25 = $3.50 X 3 + rate X 33 miles

$35.25 = $3.50 X 3 + $0.75/mile X 33 miles

$35.25 = $35.25