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Y = Costo de un caso
XY = 1000; X = 1000/Y
X + 10 = 10 sacos mas
Y - 5 = Costo de cada saco
(X + 10)(Y - 5) = 1000
XY - 5X + 10Y - 50 = 1000;
1000 - 5X + 10Y - 50 = 1000
10Y - 5X = 1000 - 1000 + 50
10Y - 5X = 50;
10Y - 50 = 5X; Simplifico por 5
X = 2Y - 10 Reemplazo X = 1000/Y
[1000/Y] = 2Y - 10
1000 = Y(2Y - 10)
1000 = 2Y² - 10Y
2Y² - 10Y - 1000 = 0; Simplifico por 2
Y² - 5Y - 500 = 0; donde a = 1; b = -5; c = -500
Y1 = [5 + 45]/2 = 25
Y2 = [5 - 45]/2 = -20
Tomo Y = 25
Costo de un Saco 25 soles.
Numero de sacos = 1000/25 = 20 sacos