Riddle about amusement park profit in relation to ticket's price Price of the ticket at amusement park was cut down. In the result there was 50% more visitors in the park. At the same time profit from tickets' sale raised by 20%.
What was the rebate for the ticket(how much ticket's price went down)?
My solution:
variables:
x - ticket' price
y - number of people who have visited the park before price cut 
z - price cut(rebate) 
Equasion:
$$
(1-z)x \cdot 1,5y=1,2xy
$$
$$
z = 0.2
$$
Thus ticket price wen down by 20%.
Question: Am I right? It seems bit too easy.

What you know is that
$$
\text{The new income} = 120\%\text{ of the old income}
$$
The new income is price per ticket, which is $(1-z)x$, times the number of tickets sold, $1.5y$. So your left hand side is good.
The old revenue was the old price of tickets, $x$, times the old number of guests, $y$. Multiply by $1.2$ to get the increase of $20\%$. All in all you get
$$
(1-z)x\cdot 1.5y = 1.2xy
$$
which is exactly your equation.
If it seems easy it's only because you found the elegant way of solving it and / or this is an elegantly posed problem. Finding solutions like this is part of the joy of mathematics for many people, including me.
