What is the answer for this question: Divide 100 loaves of bread among five men so that the amounts are in aritmetic progression (increase by the same amount each time) and the sum of the 3 largest is 7 times the amount of the 2 smallest
Since it is an arithmetic progression, the middle number must be 20.
Try 0, 10, 20, 30, 40
7*sum of lowest 2 = 70
Sum of largest 3 = 90
Try 2,11,20,29,38
7*sum of lowest 2 = 91
Sum of highest 3 = 96
I don't think this can be solved with numbers of loaves that are all integers.
If a is the separation of adjacent numbers,
7*(40 - 3a) = 60 + 3a
220 = 24 a
a = 9 1/6
That makes the numbers 1 2/3, 10 5/6, 20, 29 1/6 and 38 1/3