SOLUTION: My mom and I can't figure out how to solve this word problem. Producing a musical costs $88,000 plus $5900 per performance. One sold-out performance earns $7500 in revenue. If ev

Click here to see ALL problems on Linear-systems

Question 538670: My mom and I can't figure out how to solve this word problem.
Producing a musical costs $88,000 plus $5900 per performance. One sold-out performance earns $7500 in revenue. If every performance sells out, how many performances are needed to break even?
Here is what we tried:
y=7500x + 5900 y=88000
88000= 7500x + 5900
82100=7500x
10.94 shows
also tried:
x= 7500 x= 88000+5900
x=93900/7500
12.52 shows
I know I am doing something wrong. I'm really confused!
Answer by jpg7n16(66) (Show Source):
You can put this solution on YOUR website!
Okay, let's start by taking the original problem and breaking it up into managable equations.
.
"Producing a musical costs $88,000 plus $5900 per performance."
.
Let's start there. Let's call the cost of the musical "C" and each performance "P." How do you turn that statement into an equation?
1)
Cost=88,000 plus $5900 per Performance
.
"One sold-out performance earns $7500 in revenue."
.
Let's call revenue "R". So total revenue would be $7500 per performance. As an equation:
2)
.
Now we have our formulas.
.
"If every performance sells out, how many performances are needed to break even?"
.
We know that you break even when your Revenues equal your costs, right? So when: the show will break even. That means we can set equations R and C equal to each other and solve for the number of performances P

.
Therefore, the musical will break even after 55 sell out performances.
.
.
As a faster, easier way - you could just say that . You make 7500 per show, costs 5900/show. And you started in the hole $88k.
You're making back - per show
.
shows to make your money back