The physical education instructor during Cream of the Crop paid for the bucket of watermelons for $200. She labelled the melons so which she would have $1.50 distinction upon any melon. When all though thirty had been sold, the physical education instructor had recovered her primary investment. How most did she buy originally?
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let the amount of watermelons bought be x.
let the original price the watermelons were bought at be y.
construct two equations:
xy = 200 ………(1)
(y + 1.5) (x – 30) = 200 ………(2)
Then solve simultaneously
(y + 1.5) (x – 30) = xy
xy – 30y + 1.5x – 45 = xy
-30y + 1.5x = 45
x = 30 + 20y
sub back into (1):
(30 + 20y)y = 200
30y + 20y^2 = 200
20y^2 + 30y – 200 = 0
quadratic equation (maybe you can factorize it, but I just used the equation):
y = 2.5 or -4
since y cannot be a negative value, y = 2.5, ie the original price was $2.50
sub back into (1):
2.5x = 200
x = 80
therefore she bought 80 watermelons originally