SOLUTION: A merchant paid $1,800 for a group of men's hat. He sold all but 5 of the hats at $20 more per hat than he paid, thereby making a profit of $200 on the transaction. How many hats d

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Question 308987: A merchant paid $1,800 for a group of men's hat. He sold all but 5 of the hats at $20 more per hat than he paid, thereby making a profit of $200 on the transaction. How many hats did the merchant buy?
choices:
A:)20
B:)25
C:)30
D:)35
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let h=number of hats he bought.
1800/h cost of each hat
(1800/h)+20 sale price of each hat
h-5 number of hats he sells
2000 income from the sale of the hats
.
((1800/h)+20)(h-5)=2000
(1800+20h)(h-5)=2000h multiply each side by h to eliminate fraction.
20h^2+1700h-9000=2000h
h^2+85h-450=100
h^2-15h-450=0
(h-30)(h+15)=0
h=30 number of hats he bought.
.
Ed