A train ticket in a certain dty is 200 People who use the tr

A train ticket in a certain dty is $2.00. People who use the train also have the option of purchasing a frequent rider pass for $15.75 each month. With the pass, each ticket costs only $1.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the total monthly cost with the pass. 20 times 22 times 23 times 21 times

Solution

let us assume x = number of rides per month.
Without the pass, the cost per ride is 2.00 per ride.
With the pass, the cost per ride is 1.25 per ride plus 15.75 per month.
The formula for total cost is as follows:

without the pass:
C1 = 2*x

with the pass:
C2 = 15.75 + 1.25*x

You want to know when C2 becomes equal to C1.
15.75 + 1.25*x = 2*x
Subtract 1.25*x from both sides of this equation to get:
15.75 = 2*x - 1.25*x which becomes:
15.75 = .75*x
Divide both sides of this equation by .75*x to get:
15.75/.75 = x
21 = x  
therefore number of rides per month=21