The Horse and the Donkey
A donkey and a horse are carrying some bags of rice and some bags of beans.
The horse tells the donkey: "If you give me a bag of rice, then I would have twice as many bags of rice as you would, but if I give you one bag of rice instead, we will have the same number of bags of rice."
He continued, "Also, if you give me one bag of beans, I will have twice as many bags of beans but if I give you 2 bags of beans we will have the same number of bag of beans."
How many bags in total does the horse have?
Inspired by a problem a cousin gave me.
The answer is 18.
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1 solution
Let x , y , z and w be as follows:
x = number of bags of rice the horse is carrying.
y = number of bags of rice the donkey is carrying.
z = number of bags of beans the horse is carrying.
w = number of bags of beans the donkey is carrying.
⇒ we have two systems of equations:
x + 1 = 2 ( y − 1 ) , x − 1 = y + 1 and z + 1 = 2 ( w − 1 ) , z − 2 = w + 2 ⇒ y = x − 2 ⇒ x + 1 = 2 ( x − 3 ) = 2 x − 6 ⇒ x = 7 . Using similar algebra we get z = 1 1 . Then the horse has x + z = 1 8 .