Question 101691
you are starting a business selling boxes of hand-painted greeting cards. to get started, you spend $36 on paint and paintbrushes that you need. You buy boxes of plain cards for $3.50 per box, paint the cards, and then sell them for $5 per box. how many boxes must you sell for your revenue to equal your expenses? 
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Let x = number of boxes of cards
:
Cost equation consist of the cost per box times no. of boxes + the fixed cost
Cost = 3.5x + 36
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The revenue equation is the number of boxes times the retail price per box
Revenue = 5x
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Break even point occurs when Revenue = cost, so we have:
5x = 3.5x + 36
Simple algebra finds x
5x - 3.5x = 36
1.5x = 36
x = 36/1.5
x = 24 boxes
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Another words, when you sell 24 boxes you will pay your expenses
:
It also asks:
"What will your revenue and expenses equal when you break even?"
Substitute 24 for x in both equations
:
5 * 24 = $120 is the revenue
and
3.5(24) + 36
84 + 36 = $120 is the expense
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That's not too difficult to understand, is it?