1550.43 – A Horse and a Mule Converse

Tags:Problem Set 11GeometryAlgebra Prep

They had just finished carrying a heavy load into town: bags of gold dust mined from their Yosemite River claim. After a bucket of beer each, they had this conversation.

The Horse: Am I beat! My load is soooo heavy!

The Mule: Hey man! My load was heavier than yours. So much heavier that if I gave you one of my bags we’d have ended up carrying the same load.

The Horse: Aww shucks. I have chilblains in my left off fore knee; my stomach aches from the rotten hay we had for dinner; and I’m losing my right hind shoe. And did I mention my forelock? It needs a shampoo real bad.

The Mule: My heart bleeds for you. Still, if I took just one bag off you, I’d have been carrying twice your load. That shore wouldn’t have been fair, now would it, podner?

How many bags did each have?


Let H and M be the number of bags of gold dust that horse and mule, respectively, were carrying. From the mule’s first speech, we learn that

H + 1 = M – 1,

so M = H + 2. From the mule’s second speech, we learn that

M + 1 = 2 (H – 1).

Putting these together, H + 3 = 2 H - 2, so H = 5 and M = 7. Voila!