Question

Ninety passengers rode in a train from City A to City B. Tickets for regular coach seats cost ​$121. Tickets for sleeper car seats cost ​$285. The receipts for the trip totaled ​$19,418. How many passengers purchased each type of ticket?

(a) 60 regular coach seats, 30 sleeper car seats
(b) 30 regular coach seats, 60 sleeper car seats
(c) 45 regular coach seats, 45 sleeper car seats
(d) 50 regular coach seats, 40 sleeper car seats

Answer 1

By setting up a system of equations with two variables, x and y, representing the number of regular coach and sleeper car seats sold respectively, and solving it, we find that 38 passengers purchased regular coach seats and 52 passengers purchased sleeper car seats.

Step-by-step explanation:

To determine how many passengers purchased each type of ticket, we must set up a system of equations based on the information given:

• Let x be the number of regular coach seats sold.
• Let y be the number of sleeper car seats sold.
• We know that x + y = 90 because there are 90 passengers in total.
• We also know that the total revenue is $19,418, so 121x + 285y = 19418.

We can now solve this system using substitution or elimination. Let's use the substitution method:

1. From the first equation, y = 90 - x.
2. Substitute y in the second equation: 121x + 285(90 - x) = 19418.
3. Simplify and solve for x: 121x + 25650 - 285x = 19418, which simplifies to 164x = 6232.
4. Divide by 164 to find x: x = 38.
5. Substituting x back into y = 90 - x gives us y = 90 - 38 = 52.

Therefore, 38 passengers purchased regular coach seats and 52 passengers purchased sleeper car seats, which corresponds to option (b).