Page:The Rhind Mathematical Papyrus, Volume I.pdf/100

84 SECTION VIII

Problem 39

Example of finding the difference of share when 100 loaves are divided among 10 men, 50 in equal shares among 6 men and 50 in equal shares among 4. What is the difference of the shares?

Multiply 4 so as to get 50.

Multiply 6 so as to get 50.

Therefore each of the 4 will receive 12$1/undefined$ and each of the 6will receive 8$1/undefined$, and the difference of share will be 4$1/undefined$.

Problem 40

Divide 100 loaves among 5 men in such a way that the shares received shall he in arithmetical progression and that $1/undefined$ ''of the sum of the largest three shares shall he equal to the sum of the smallest two. What is the difference of the shares?''

Do it thus: Make the diﬂerence of the shares 5$1/undefined$. Then the amounts that the 5 men receive will be

2317$1/undefined$126$1/undefined$1, total 60.