Question

Person 1 and Person 2 visited Washington D.C. for the weekend. Person 1 rode the metro train one stop, 5 times at the peak fare price and 3 times at the off peak fare price for a total cost of $21.00. Person 2 rode with Person 1 four times at the peak fare price and twice at the off peak fair price for a total cost of $16.00. How much was the peak fare price?​

Answer 1

Answer: Let's use P to represent the peak fare price and O to represent the off-peak fare price. We can set up two equations based on the given information:

5P + 3O = 21 (equation 1)

4P + 2O = 16 (equation 2)

We can simplify equation 2 by dividing both sides by 2:

2P + O = 8 (simplified equation 2)

Now we can use either substitution or elimination method to solve for one variable. Let's use substitution method by solving equation 2 for O in terms of P:

O = 8 - 2P (solving for O in equation 2)

Now we can substitute this expression for O into equation 1 and solve for P:

5P + 3O = 21

5P + 3(8 - 2P) = 21 (substituting for O)

5P + 24 - 6P = 21 (distributing the 3)

-P + 24 = 21 (combining like terms)

-P = -3

P = 3

Therefore, the peak fare price is $3.

Explanation: