The fourth with 4 workmen will have
13'1⁄41⁄1/161⁄64 hekat 12⁄3ro or 131⁄3 hekat
The four with 30 workmen will have 100 hekat " 100 "
This problem is merely to divide 100 into four parts proportional to the numbers 12, 8, 6,and 4. The laborious numerical calculations are due to the use of the "Horuseye" fractions. See Introduction, pages 31-32.
The solution was lengthened in the papyrus also by much repetition. In particular, the multiplication of 31⁄41⁄161⁄64 hekat 11⁄3ro was carried out four times. as far as 8 twice, and as far as 4 twice, the required products being checked and the total put down for each of the four overseers.
Problem 69 introduces the word pefsu, and Problems 69——78 are problems about pefsu. This word is derived from the stem of the verb "to cook." It meant something like "cooking ratio," that is, the number of units of food or drink that could be made from a unit of material in the process of cooking, and it determined the relative value of any food or drink. To preserve the technical sense I will use the word pefsu in my translation. We may note that the lower the pefsu the more valuable the unit of food.
The pefsu problems are very simple examples in arithmetic, made to seem more abstruse by the use of this word pefsu, and, in some of them, by the use of the word "exchange." We shall see that they can be stated in a way that will make explanations almost unnecessary.
Problem 69
31⁄2 hekat of meal is made into 80 loaves of aread. Let me know the amount of meal in each loaf and what is the pefsu.
Multiply 31⁄2 so as to get 80.
| 1 | 31⁄2 | |||||||
| 10 | 35 | \ | 20 | 70 | \ | 2 | 7 | |
| \ | 2⁄3 | 21⁄3 | ||||||
| \ | 1⁄21 | 1⁄6 | ||||||
| \ | 1⁄7 | 1⁄2 |
The pefsu is 222⁄31⁄71⁄21.
