Question

Divide 100 loaves of bread among five men so the amount is arithmetic sequence and the sum of the largest is seven times the amount of the two smallest.

Answer 1

first equation:
a + a+d + a+2d + a+3d + a+4d = 100
5a + 10d = 100
a + 2d = 20 or a=20-2d

2nd equation
a+4d = 7(a + a+d)
a+ 4d = 14a + 7d
13a =-3d

13(20-2d) = -3d
260 - 26d = -3d
260 = 23d
d = 260/23 (or appr 11.3)
a = 20 - 520/23 = -60/23 (or appr. -2.6 ????)

Mathematically, these answers work for the above condition, but they don't make any real sense.

Check:
first gets -2.6
2nd gets 8.7
3rd gets 20
4th gets 31.3
5th gets 42.6 , they form an arithmetic sequence
(-2.6+8.7+20+31.3+42.6 = 100)

7 times the first two = 7(-2.6+8.7) = 42.7
the last one = 42.6 (close enough, error due to roundoff)

Something is wrong with your question!