Question 538670
Okay, let's start by taking the original problem and breaking it up into managable equations.
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"Producing a musical costs $88,000 plus $5900 per performance."
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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) {{{c=88000+5900*p}}}
Cost=88,000 plus $5900 per Performance
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"One sold-out performance earns $7500 in revenue."
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Let's call revenue "R". So total revenue would be $7500 per performance. As an equation:
2) {{{r=7500*p}}}
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Now we have our formulas.
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"If every performance sells out, how many performances are needed to break even?"
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We know that you break even when your Revenues equal your costs, right? So when: {{{R=C}}} 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
{{{88000+5900p=C=R=7500p}}}
{{{88000+5900p=7500p}}}
{{{88000=1600p}}}
{{{1600p=88000}}}
{{{p=88000/1600=55}}}
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Therefore, the musical will break even after 55 sell out performances.
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As a faster, easier way - you could just say that {{{profit = revenue - cost}}}. You make 7500 per show, costs 5900/show. And you started in the hole $88k.
You're making back {{{7500-5900=1600}}} - per show
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{{{88000/1600=55}}} shows to make your money back