Page:The Rhind Mathematical Papyrus, Volume I.pdf/118

102 Problem 64

''Example of determining an arithmetical progression. Suppose it is said to thee, Distribute 10 hekat of barley among 10 men in such a way that the shares shall he in arithmetical progression with a common difference of $1/undefined$, hekat. What is the share of each?''

The average share is 1 hekat. The number of differences will be 9, 1 less than the number of men. Take $1/undefined$ of the common difference; it makes $1/undefined$ hekeat. Multiply this by 9; it makes $1/undefined$$1/undefined$ hekat. Add it to the average share; 1$1/undefined$$1/undefined$ hekat is the largest share. Subtract the $1/undefined$ hekat for each man until you reach the last.

Do it thus: The ten portions will be 1 $1/undefined$$1/undefined$, 1$1/undefined$$1/undefined$$1/undefined$, 1$1/undefined$$1/undefined$, 1$1/undefined$$1/undefined$, $1/undefined$$1/undefined$$1/undefined$$1/undefined$, $1/undefined$$1/undefined$$1/undefined$, $1/undefined$$1/undefined$$1/undefined$, $1/undefined$$1/undefined$, $1/undefined$$1/undefined$$1/undefined$.

The total is 10 hekat.

Problem 65

Example of dividing 100 loaves among 10 ''men, including a boatman, a foreman, and a door-keeeper, who receive double portions. What is the share of each?''

The working out. Add to the number of the men 3 for those with double portions; it makes 13. Multiply 13 so as to get 100; the result is 7$2/3$$1/undefined$. This then is the ration for seven of the men, the boatman, the foreman, and the door-keeper receiving double portions.

For proof we add 7$2/3$$1/undefined$ taken 7 times and 15$1/undefined$$1/undefined$$1/undefined$ taken 3 times for the boatman, the foreman, and the door-keeper. The total is 100.

Problem 66

If 10 hekat of fat is given out for a year, what is the amount used in a day?

The working out. Reduce the 10 hekat to ro; it makes 3200. Reduce the year to days; it makes 365. Get 3200 by operating on 365. The