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Question 692970: The cost of producing an item is $5 per item plus an initial cost $2000. The selling price is $10 per item . Find the break- even point
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! The break-even point is when the expenses and revenues come together to literally "break-even", or when the the income meets the level of payout for a business or economy. In these basic algebra problems, it is good to name the two sides of the equation we will be dealing with. Let one side be the "income" and let the other be "expenses". All we need to do is put the income term(s) on one side and the expense term(s) on the other. If we have more than one of a term on a side of an equation, we add them together. In our problem, we have an initial cost of $2000, or what is known as our constant, and we have expenses of $5 for each item we produce ($5x). We add these terms together on one side of the equation. The other side of our equation will be the income term, or $10 an item that we sell ($10x). Now we solve for x:
$5x + $2000 = $10x
$2000 = $5x
x = 400 items.
So we need to make and sell 400 items in order for our revenues to reach the level of expenses. The 401th item should cause us to start receiving profit if no other variable or constant is added into the expenses category.
To know where our variable should be place, we need to figure out where the statement says something along the lines of "per item" or "for each of something". In this case, we had $5 "for each item" produced and $10 "for each item" sold. To know what which is an expense term and which is an income term, we need to figure out what is costing us and what is making us gain money.
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