SOLUTION: You're choosing between 2 plans at a discount warehouse. PLAN A: annual membership fee is $100 and you pay 80%of manufacturer's recommended list price. PLAN B: annual membership fe

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Question 109815: You're choosing between 2 plans at a discount warehouse. PLAN A: annual membership fee is $100 and you pay 80%of manufacturer's recommended list price. PLAN B: annual membership fee is $40 and you pay 90% mrlp. How many dollars of merchandise would you need to buy in a year to pay the same amount under both plans? What will be the cost for each plan?--------Can someone please help me with this problem? I don't know how to set this up or solve it algebraically. Thank you so much.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
At some point in your purchases the two plans will cost the same. After that point Plan A (the
plan with the higher initial cost of $100) will save you money.
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Suppose we let P represent the manufacturers' recommended prices for items. Under Plan B
your cost would be $40 + 0.90*P for all the items that you buy.
.
Under Plan A your cost would be $100 + 0.80*P for all the items that you buy.
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Set these two costs equal and you get:
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40 + 0.90*P = 100 + 0.80*P
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Let's collect the terms containing P on the left side and the constants on the right side.
Begin by getting rid of the 40 on the left side by subtracting 40 from both sides to get:
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0.90*P = 60 + 0.80*P
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Then get rid of the 0.80*P on the right side by subtracting 0.80*P from both sides to reduce
the equation to:
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0.10*P = 60
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Finally solve for P by dividing both sides of this equation by 0.10 (or by multiplying
both sides by 10) to arrive at:
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P = 60/0.1 = 600
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This tells you that when you buy $600 worth of goods at the Manufacturers' suggested retail
prices, the cost under both plans will be the same.
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Let's check that out. Plan A would cost you $40 + 90% of 600 and this is equal to $40
+ 0.9*600 = $40 + $540 = $580. Had you signed up for Plan B, when you bought $600 of merchandise
you would have spent $580.
.
How about Plan A. If you bought $600 worth of merchandise under Plan A you would have spent
a total of $100 plus 80% of $600. So you would have spent $100 + $480 = $580.
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So that's your answer. If you plan on spending more than $600 at the manufacturers'
prices you will save money by going with Plan A. Let's check this by saying that we bought
$1000 worth of items for the year. Under Plan B the cost would be $40 + 0.9*1000 = $40 + $900 = $940.
But under Plan A the cost would be $100 + 0.8*1000 = $100 + $800 = $900. So you would save
about $40 by going with Plan A.
.
Hope this helps you to understand the problem and to see what is going on with the equations.
.