SOLUTION: A train ticket in a certain city is $1.50. People who use the train also have the option of purchasing a frequent rider pass for $16.50 each month. With the pass, each ticket costs

Question 1199791: A train ticket in a certain city is $1.50. People who use the train also have the option of purchasing a frequent rider pass for $16.50 each month. With the pass, each ticket costs only $0.75. 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.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Option A: No monthly pass
Option B: Monthly pass

x = number of times the person rides the train
y = total cost after riding x times

The cost equation for option A is
y = 1.50x

The cost equation for option B is
y = 0.75x+16.50

Use substitution to solve for x.
1.50x = 0.75x+16.50
1.50x-0.75x = 16.50
0.75x = 16.50
x = 16.50/0.75
x = 22
The costs are the same when the person rides the train 22 times.

Check:
y = 1.50x = 1.50*22 = 33 dollars is the cost of option A
y = 0.75x+16.50 = 0.75*22+16.50 = 33 dollars is the cost of option B
Each option yields the same cost, which confirms the answer.

Answer: 22

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