A horse and a mule were traveling together heavily laden with bags of golden trinkets. After a time, the mule complained to the horse that his load was too heavy. “What’s the matter?” said the horse. “You shouldn’t complain, for had I taken one of your bags I would have had to carry twice as many bags as you. On the other hand, if you agreed to take one of mine, we’d have the same number of bags.” How many bags did each have?
| horse | mule | horse + 1 ≟ | 2 x (mule – 1) |
| 3 | 1 | 4 | 0 |
| 4 | 2 | 5 | 1 |
| 5 | 3 | 6 | 2 |
| 6 | 4 | 7 | 3 |
| 7 | 5 | 8 | 4 |
From the second statement we see that the horse has two more bags than the mule. If we assume that the number of bags is small, we can make a chart and record guesses.
Or using algebra:
x is the number of the horse’s bags,
x – 2 is the number of the mule’s bags:
x + 1 = 2(x – 2 – 1)
x + 1 = 2x – 6
x = 7.
Either way, the horse has 7 bags and the mule has 5.