Find the excess of 45 over 10; it is 35. Multiply 10 so as to get 35; it makes 31⁄2. Multiply 100 by 31⁄2; it makes 350. Add 100 thereto; it makes 450. Say then that there are exchanged 100 loaves of pefsu 10 for 450 loaves of pefsu 45, making in wedyet-flour 10 hekat.
In this Problem our author asks the question, If one has 100 loaves with a pefsu of 10, for how many loaves with a pefsu of 45 can he exchange them? He arrives at the result in a round-about way. He could simply have determined that 10 hekat, the amount of meal required to produce the given 100 loaves, would have produced 10 times 45 loaves of the second kind, and he would thus have arrived at the same result. This is the way in which he solves the next problem and Problem 75, both of which are problems of the same kind.
Problem 73
Suppose it is said to thee, 100 loaves of pefsu 10 are to be exchanged for loaves of pefsu 15. How many oftlzese will there be?
Reckon the amount of wedyet-flour in these 100 loaves; it is 10 hekat. Multiply 10 by 15; it makes 150. This then is the number of loaves for the exchange.
Do it thus: 100 loaves of pefsu 10 would be exchanged for 150 loaves of pefsu 15. It takes 10 hekat.
As in Problem 72, 100 loaves of pefsu 10 require 10 hekat of wedyey-flour, for "pefsu 10" means that 1 hekat makes 10 loaves. Now in this problem a hekat will make 15 loaves of the second kind, and so 10 hekat will make 150 loaves. Therefore 150 loaves of the second kind will be the equivalent of the 100 given loaves of the first kind.
Problem 74
Another problem. 1000 loaves of pefsu 5 are to be exchanged a half for loaves of pefsu 10, an a half for loaves of pefsu 20.
How many of each will there be?
1000 loaves of pefsu 5 will take 200 hekat of Upper Egyptian barley. This then is the amount of wedyet-flour in these loaves. 1⁄2 of the 200 hekat is 100 hekat. Multiply 100 by 10; it makes 1000, the number of loaves of pefsu 10. Multiply 100 by 20; it makes 2000, the number of loaves of pefsu 20.
Do it thus: 1000 loaves of pefsu 5, made from 200 hekat of wedyet-flour, can be exchanged for 1000 loaves of pefsu 10, taking 100 hekat, and 2000 loaves of pefsu 20, taking 100 hekat.
In this problem the given 1000 loaves require 200 hekat of wedyet-flour. Then, if the same amount is used to make two kinds of loaves, one-half of it at the rate of 10 loaves to a hekat. and the other half at the rate of 20 loaves to a hekat, the result will be 1000 loaves of the first kind and 2000 loaves of the second kind.
