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)

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