Sunday, February 16, 2014

Dante's Infernal Puzzle Collection -- 19. Grana

Suppose he sold x of units of the poor grains and y units of the fair grains.
His cost was 32x + 40y.
He sold x + y units of grains at the price of 43, so his revenue was 43x + 43y.

(32x + 40y) * (1.25) = 43x + 43y
40x + 50y = 43x + 43y
3x = 7y
x = (7/3)y

Suppose x + y = 100.
(7/3)y + y = 10/3y = 100
y = 30
x = 100 - 30 = 70

Thus, 70% of the grains he sold were poor, and 30% were fair.

Answer: 70% poor, 30% fair

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