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ACCOUNTING

Audio sells headphones and would like to earn after tax profit of $400 every week. Each set of headphones costs $5 and is sold for $10. They also incur costs of $200 for rent and other fixed costs, and their tax rate is 20%. How many headphones must they sell per week to meet this goal?
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1 Answer

Let h = # headphones
 
Assuming the tax rate applies on the revenue of 10h:
 
Cost:  5h + 200
Revenue: 10h - .2(10h) = 8h
 
8h - (5h + 200) = 400
8h - 5h - 200 = 400
3h = 600
h = 200
 
If we sell 200 headsets we make $400
----------------------------------------------------
 
Check:  Revenue = 10h = $2000
Cost: rent:  $200
         taxes: .2(2000) = $400 
         headphone cost: 5h = $1000
         Total Cost = $1600
 
Profit = revenue - cost = 2000 - 1600 = $400

Comments

Note:  This assumes that we did not incur further
expenses by purchasing more headphones than
we sold... 
 
If we purchased 20 headphones and only sell
10 we have less profit...