Question

the performing arts department put in its spring show on Friday and Saturday nights. the price of a ticket was the same both nights. the department made a profit of 400 on friday when 100 people bought tickets, and 500 on saturday when 120 people bought tickets. how much did one ticket cost? what was the cost of putting on the show?

Answer 1

Let $p=$ the price of a ticket
Let $c=$ the cost to put on the show

Formula:
(profit) = (ticket price) * (number of people) - (cost to put on show)
We have two equations here:
$500=120p-c$
$400=100p-c$
Solve:
$100=20p$
⇒$p=5$
⇒$400=100(5)-c$
⇒$400=500-c$
⇒$c=100$

So the price of a ticket is $5, and the cost to put on the show is $100.