That is, one of the loaves contains 251⁄5ro, or 1⁄161⁄64 hekat 1⁄5 ro.
Proof.
| 1 | 1⁄161⁄64 hekat 1⁄5 ro | ||||
| 10 | 1⁄21⁄41⁄32 | " | 2 | " | |
| 100 | 71⁄21⁄41⁄8 | " |
This problem is similar to the preceding. The reduction of the given number of hekat to ro is omitted in the papyrus, but the result, 2520, is given, and given as if it were the result of the multiplication used to prove the first part of the solution. Evidently, in copying this solution, the scribe let his eye drop from one "Total" to the next, and so left out the result of one multiplication and all the partial products of the next (Feet, page 116). See note to Problem 28.
There are some interesting steps in the first multiplication and in the first proof.We may notice also that in the first multiplication, as also in Problem 69, we have the "Horus eye" fractions given in the statement of the problem written as ordinary fractions. See Introduction, page 31, footnote 3.
Problem 71
From 1 des-measure of beer 1⁄4 has been poured of, and then the measure has been filled up with water. What is the pefsu of the diluted beer?
Reckon the amount of besha[1] in 1 des of beer; it is 1⁄2 hekat. Take away 1⁄4 of it, namely 1⁄8 hekat; the remainder is 1⁄41⁄8 hekat. Multiply 1⁄41⁄8 hekat so as to get 1 hekat; the result is 22⁄3, and this is the pefsu.
The solution as given means that when besha is made into beer, 1⁄2 hekat of besha will make 1 des-jug of beer. If the beer is made weaker by pouring off 1⁄4 of it and filling with water, it will take less besha by 1⁄4 to make enough of this diluted beer to fill the jug, namely, 1⁄41⁄8 hekat, and so 1 hekat of besha will make 22⁄3 des of this weaker kind of beer. Pefsu then means here the number of des-jugs of beer that a hekat of besha will make, just as in the preceding two problems it means the number of loaves that a hekat of meal will make.
The first 1⁄2 hekat in the solution is written by mistake in the papyrus as an ordinary 1⁄2. Elsewhere the fractions of a hekat are written in the "Horus eye" form.
The mention of besha and of other kinds of food may tend to make these solutions seem more obscure, but in no way do they have anything to do with the reasoning or numerical work, and we can leave them out of consideration in trying to understand this.
Problem 72
Example of exchanging loaves for other loaves. Suppose it is said to thee, 100 loaves of pefsu 10 are to be exchanged for a number ofloaves ofpefsu 45. How many of these will there he?
- ↑ For a list of kinds of grain or food mentioned in the papyrus see Introduction, page 46.
