SOLUTION: A store bought a $1000 shipment of sweaters and offered them for sale after a $15 markup on each sweater. All but 10 sweaters were sold, and the store made a $400 profit on the swe

Question 77572: A store bought a $1000 shipment of sweaters and offered them for sale after a $15 markup on each sweater. All but 10 sweaters were sold, and the store made a $400 profit on the sweaters. How many sweaters did the store buy?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A store bought a $1000 shipment of sweaters and offered them for sale after a $15 markup on each sweater. All but 10 sweaters were sold, and the store made a $400 profit on the sweaters. How many sweaters did the store buy?
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Let "x" be the number of sweaters bought.
Paid price per sweater = 1000/x
Selling price per sweater = 1000/x + 15
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EQUATION:
(number of sweaters sold)(selling price) = 1000 +400
(x-10)((1000/x)+15)=1400
1000+15x-10000/x-150 = 1400
15x-(10000/x)=550
15x^2-10000=550x
15x^2-550x-10000=0
3x^2-110x-2000=0
x=[110+-sqrt(12100-4*3*-2000)]/6
x=[110+-sqrt(36100)]/6
x=50 (# of sweaters bought)
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Cheers,
Stan H.
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