Problem 62
Example of reckoning the content: of a bag of various precious metals. Suppose it is said to thee, .4 bag containing equal weights of gold, silver and lead, has been bought for 84 sha'ty. What is the amount in it of each precious metal, that which is given for a deben of gold being 12 sha'ty, for a deben of silver 6 sha'ty, and for a deben of lead 3 sha'ty?
Add that which is given for a deben of each precious metal. The result is 21 sha'ty. Multiply 21 so as to get 84, the 84 sha'ty for which this bag was bought. The result is 4, which is the number of deben of each precious metal.
Do it thus:
| Multiply | 12 by 4 getting 48 sha'ty for the gold in the bag, |
| Multiply | 6 by 4 getting 24 sha'ty for the silver, |
| Multiply | 3 by 4 getting 12 sha'ty for the lead, |
| Multiply | 21 by 4 getting 84 sha'ty altogether. |
The sha'ty was a seal, and the word here represents a unit of value (see Weill, 1925). The deben was a unit of weight, equal to about 91 grammes. The papyrus does not say that the bag contains equal weights of gold, silver, and lead, but in the solution the author proceeds as if this condition was understood.
Problem 63
Example of dividing 700 loaves among four men in the proportion of the numbers 2⁄3, 1⁄2, 1⁄3 and 1⁄4. Let me know the share that each man receives.
Add 2⁄3, 1⁄2, 1⁄3 and 1⁄4; it makes 11⁄21⁄4. Get 1 by operating on 11⁄21⁄4; it makes 1⁄21⁄4. Take M 1⁄21⁄4 of 700; it is 400. 2⁄3,1⁄2,1⁄3 and 1⁄4 of 400 will give the shares of the four men.
Do it thus:
| The quantity is | 700 | |
| 1⁄21⁄14 | of it is | 400 |
| 2⁄3 | of 400 to one is | 2662⁄3 |
| 1⁄2 | of 400 to one is | 200 |
| 1⁄3 | of 400 to one is | 1331⁄3 |
| 1⁄4 | of 400 to one is | 100 |
| Total | 700. | |
