SOLUTION: If the item sells retail for $15.00 and has a cost of $3.00 it would leave a profit of $12.00. When six of this item are purchased at the same time there is a discount of $.50 per

Question 493635: If the item sells retail for $15.00 and has a cost of $3.00 it would leave a profit of $12.00. When six of this item are purchased at the same time there is a discount of $.50 per item. Purchasing 12 items would give a $1.00 discount per item. At what point would the amount of items purchased at one time become a loss instead of a profit?

Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
This is more a logic problem than an algebra one, but here goes...
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At 1 unit sold, we have a $12 profit. At 6 units sold, by allowing a volume discount, we erode the profit by $0.50. At 12 units old, we increase the discount by $0.50 and thus have eroded the profit by a full $1.
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Though not explicitly stated that the volume discount continues to increase, the problem implies it does by asking us when we have eliminated the profit by increasing hte size of the sale (in terms of # units sold).
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If 12 units sold erode the profit by $1, how many 12-unit jumps in discount based upon volume of sales will erode the original $12 profit? Easy answer: 12. But that is the zero profit point. To answer the original question, how many units sold will result in a loss? We need to multiply 12 x 12 to arrive at 144 units sold at one time for the break even point.
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Since the discounts are applied in blocks of 6 units sold, from 144 units sold up to 149 units sold, the $12 per-unit discount is still applied; however, when we get to 150 units sold, we trip the next $0.50 discount, making the total discount $12.50 > the original profit of $12.00, we are now losing money on all sales.
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The answer to the problem as stated is equal to or greater than 150 units sold at one time.

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