SOLUTION: The manager at Cream of the Crop bought a load of watermelons for $180. She priced the melons so that she would make $1.50 profit on each melon. When all but 20 had been sold, the

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Question 341161: The manager at Cream of the Crop bought a load of watermelons for $180. She priced the melons so that she would make $1.50 profit on each melon. When all but 20 had been sold, the manager had recovered her initial investment. How many did she buy originally?

I am totally confuse with this word problem. I can't for the life of me figure it out, so can somone please help me.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let her buy x melons.
so cost of 1 melon = 180/x
..
she sold each at (180/x) + 1.5
when she had sold x-20 melons she got back $180
..
selling price of 1 melon * number of melons sold = 180
((180/x)+1.5)*(x-20)= 180
(180/x +3/2 )* (x-20)=180
(360+3x)/2x*(x-20)= 180
(360+3x)(x-20)= 180*2x
-7200-60x+360x+3x^2= 360x
re-arrange the terms
3x^2-60x-7200= 0
divide by 3
x^2-20x-2400=0
x^2-60x+40x-2400=0
x(x-60)+40(x-60)=0
(x-60)(x+40)=-0
So x = 60 the number of lemons she bought.