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please explain this one

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by notgoodinmath » Thu Jul 10, 2008 11:12 am
Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $420, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?

a) $2,600
b) $3,900
c) $7,800
d) $11,800
e) $18,200

please explain to me how to change this english to math!
thanks
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by wawatan » Thu Jul 10, 2008 11:30 am
this is actually a minimum and maximum problem. the trick to this problem is to minimize all the other prices so you can only maximize 1 price.

1) calculate the total cost of 25 products

total cost= 25*1200= 30000

statement 1:If none of these products sells for less than $420,
statement 2: exactly 10 of the products sell for less than $1,000

ok, the least price for all products is 420 b/c if the price is 419, it will break the statement 1 condition.

10*420=4200 cost of 10 products
1000*14= 14000 cost of 14 products
total of 14 product costs= 4200+14000= 18200
to find the cost of the most expensive product= total cost (30000)- total cost of 14 product (18200)= 11800

Answer D

the cost of the second most expensive product is 1000 b/c you know that the other 15 products is equal to or more than 1000 according to statment 2.
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