Sammy is offering to take the whole collection of 200 records and pay Peggy 4 dollars each for them which would net Peggy 200 * 4=<<200*4=800>>800 dollars for her entire record collection.

Bryan is willing to buy Peggy's entire record collection but at two different price points, half at one point and half at another.

Half of Peggy's record collection is 200/2=<<200/2=100>>100, which means that 100 records will sell for one price and 100 records will sell for another price.

Bryan is willing to pay more for the half of the record collection that he is interested in so Peggy would net 100 * 6=<<100*6=600>>600 dollars for the first half of her record collection.

For the half of the collection that Bryan is just planning on reselling at a later date, he is willing to offer Peggy 100 *1=<<100*1=100>>100 dollars to take off of her hands.

In total Bryan is willing to offer Peggy 600+100=<<600+100=700>>700 dollars for her entire record collection.

If Sammy is offering 800 dollars to buy Peggy's entire record collection and Bryan is offering 700 dollars for Peggy's entire record collection, then Peggy's net profit would be 800-700=<<800-700=100>>100 dollars more by taking Sammy's deal instead of Bryan's deal.

# Answer

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<|im_start|>system
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<|im_start|>user
Peggy is moving and is looking to get rid of her record collection. Sammy says that he will buy all of them for 4 dollars each. Bryan is only interested in half of the records but will offer 6 dollars each for the half that he is interested in and 1 dollar each for the remaining half that he is not interested in with the hopes that he can resell them in bulk later. If Peggy has 200 records, what is the difference in profit between Sammy versus Bryan's deal?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
100
Peggy is moving and is looking to get rid of her record collection. Sammy says that he will buy all of them for 4 dollars each. Bryan is only interested in half of the records but will offer 6 dollars each for the half that he is interested in and 1 dollar each for the remaining half that he is not interested in with the hopes that he can resell them in bulk later. If Peggy has 200 records, what is the difference in profit between Sammy versus Bryan's deal?
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