Algebra question?

Here's the question:

An opera house is planning to put on a performance and wants to determine its ticket prices. The theater has an orchestra section that holds 550 people, a mezzazine section that holds 140 people, and a balcony that holds 275 people. If they want a balcony seat to cost 20% less than a mezzanine seat, an orchestra seat to cost $5 more than a mezzanine seat, and a full house to bring in $16,400, how much should they charge for each type of seat?

This is what i have so far

x= orchestra seats

y = mezzanine seats

z = balcony seats

550x + 140y + 275z = 16,400

I guess i need two more equations, and this is what i have

z = y - .20

x = y + 5

Is this right? Or am I missing something else? If I do need another equation, what would it be? I plugged these two in, but it did not come out right. Thanks for your time

Algebra question?mr messed up

Here are my equations

550x+140y+275z = 16400

x = 5+y

z = 0.8y

This solves to x = 20, y = 15, z = 12