/sci/ - Science & Math

P.64: 10 numbers in arithmetic progression sum to ten. The difference between consecutive terms is 1/8. Find this solution.

Ans: {7/16,9/16,11/16,...,25/16}.

The problem is a redux of 40, this time with an odd number of terms. The mathematics is mostly the same, and a generalization is (again) pic related.

P. 65. 100 cash-money-bread are divided unequally among 10 employees. 7 of the slaves (er, employees) each gets a single share, while the other 3 happier employees receive double shares. Compute each share.

This becomes an elementary linear algebra problem entailing 2 equations with 2 unknowns, which doesn't even need gaussian elimination, simple substitution suffices. Ahmoses' method is not to do the substition that we would gravitate towards, and instead to consider "13 (primitive) shares", a natural step, and then he gets it right. The peons get 100/13, and the bigwigs get 200/13.