## 1550.43 – A Horse and a Mule Converse

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?

Solution

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!