Page:The Rhind Mathematical Papyrus, Volume I.pdf/127

78] make the same number of loaves of each kind. which makes the problem typical of a very interesting class of problems. See Introduction, page 29.

The amount given is the amount required to make 1000 loaves with a pefsu of 10; that is, it is 100 hekat. The two kinds of loaves that he wishes to get are loaves with a pefsu of 20 and loaves with a pefsu of 30. One loaf of the ﬁrst kind will take $1/undefined$ of a hekat and one loaf of the second kind will take $1/undefined$ of a hekat. He applies these fractions to 30. Perhaps he thinks of determining how much ﬂour it will take to make 30 loaves of each kind, and this he finds to be 2$1/undefined$ hekat. Now as many times as 2$1/undefined$ must be multiplied to produce 30, namely, 12 times, 1 hekat making 12 loaves of each kind, so many times must 100 be multiplied to produce the number of loaves of each kind that 100 hekat will make.

At the end in what appears to be a proof he puts down the amount of wedyel-flour that 1200 loaves of each kind will require, showing that it makes just 100 hekat. We may notice the form in which he expresses these amounts, writing the quarter and half of 100 hekat and the number of hekat in addition. This is the form used for large quantities when he would use the "Horus eye" fractions for small quantities The same forms are used in Problem 68 and in some of the problems that are to follow. See Introduction, pages 31-32.

Problem 77

''Example of exchanging beer for bread. Suppose it is said to thee, 10 des of beer (of pefsu 2) are to he exchanged for loaves of'' pefsu 5. How many loaves will there he?

Reckon the amount of wedyet-flour in 10 des of beer; it is 5 hekat. Multiply 5 by 5; it makes 25. Say then that it takes 25 loaves to make the exchange.

Do it thus:

10 des of beer taking 5 hekat of wedyet-flour can be exchanged for

25 loaves of bread of pefsu 5; for these also take 5 hekat of wedyet-flour.

Problem 78

''Example of exchanging bread for beer. Suppose it is said to thee, 100 loaves of pefsu 10 are to he exchanged for a quantity of beer of'' pefsu 2. How many des of beer will there be?

Reckon the amount of wedyet-flour in 100 loaves of pefsu 10; it is 10 hekat. Multiply 10 by 2; it makes 20. Say then that it takes 20 des of beer to make the exchange.