Question

Ninety-two passengers rode in a train from City A to City B. Tickets for regular coach seats cost $120. Tickets for sleeper car seats cost $293. The receipts for the trip totaled $19,344. How many passengers purchased each type of ticket?

The number of coach tickets purchased was _______
The number of sleeper car tickets purchased was _______

Answer 1

The number of coach tickets purchased is 44. The number of sleeper car tickets purchased is 48.

Step-by-step explanation:

Let's solve the problem using a system of equations. Let x be the number of regular coach tickets purchased and y be the number of sleeper car tickets purchased.

From the given information, we can set up the following system of equations:

x + y = 92 (equation 1)

120x + 293y = 19,344 (equation 2)

Multiply equation 1 by 120 to eliminate x:

120x + 120y = 11,040 (equation 3)

Now, subtract equation 3 from equation 2:

120x + 293y - (120x + 120y) = 19,344 - 11,040

173y = 8,304

y = 48

Substitute the value of y into equation 1 to find x:

x + 48 = 92

x = 44

Therefore, the number of coach tickets purchased is 44 and the number of sleeper car tickets purchased is 48.