Ninety-nine passengers rode in a train. Tickets for regular coach seats cost \$120, and tickets for sleeper car seats cost \$290. The total receipts for the trip were \$19,530. The problem asks to find the number of passengers who purchased each type of ticket.

1. Problem Description

Ninety-nine passengers rode in a train. Tickets for regular coach seats cost \120, and tickets for sleeper car seats cost \

2

9

0. The total receipts for the trip were \$19,

5

3

0. The problem asks to find the number of passengers who purchased each type of ticket.

2. Solution Steps

Let $x$ be the number of coach tickets purchased, and $y$ be the number of sleeper car tickets purchased. We can set up a system of two equations with two variables:

$x + y = 99$ (total number of passengers)

$120x + 290y = 19530$ (total revenue from ticket sales)

We can solve this system of equations. First, solve the first equation for $x$:

$x = 99 - y$

Substitute this expression for $x$ into the second equation:

$120(99 - y) + 290y = 19530$

$11880 - 120y + 290y = 19530$

$170y = 19530 - 11880$

$170y = 7650$

$y = \frac{7650}{170}$

$y = 45$

Now, substitute $y = 45$ back into the equation $x = 99 - y$:

$x = 99 - 45$

$x = 54$

So, the number of coach tickets purchased was 54, and the number of sleeper car tickets purchased was

4

5.

3. Final Answer

The number of coach tickets purchased was

5

4. The number of sleeper car tickets purchased was

4

5.