Question

Ninety-three passengers rode in a train from City A to City B. Tickets for regular coach seats cost $115. Tickets for sleeper cars seats cost $290. The receipts for the trip totaled $20,320. How many passengers purchased each type of ticket?

Answer 1

To solve this, we must set up a Systems of Equations problem
Let's say C stands for Coach seats bought and S stands for sleeper cars bought
Here are our equations we have enough information to make.
c + s = 93
115c + 290s = $20,320
Lets solve for Coach seats first
To do that we need a value for s
In the first equation, s = 93 - c
Lets plug that in for S in the second equation
115c + 290(93 - c) = $20,320
Distribute and simplify
115c + 26,970 - 290c = $20,320
Combine like terms
-175c + 26,970 = $20,320
-175c = -6650
divide
c =
`(-6650)/(-175)`
c = 38
We just found out 38 coach seats were bought.
Plug in 38 for C in this equation ⇒ 115c + 290s = $20,320 to find S
115(38) + 290s = $20,320
Distribute and Simplify
4,370 + 290s = $20,320
290s = $15,950
Divide
S =
`(15950)/(290)`
S = 55
We just completed the problem!
38 Coach seats were bought and
55 Sleeper car seats were bought.