Question

Divide 100 loaves of bread amoung five men so that the amounts are in arithmetic progression ( increase by the same amount each time) and the sum of the three largest is seven times the amount of the two smallest.

Answer 1

Solve the system
a+(a+d)+(a+2d)+(a+3d)+(a+4d)=100
7(2a+d)=3a+9d

Answer 2

5a+10d=100 or
a+2d=20
second equation
14a+7d=3a+9d
11a-2d=0

add equations to get
12a=20
a=20/12=5/3

then solve for d in first equation.

Answer 3

is 10/6 + 65/6 + 120/6 + 175/6 + 230/6 equal to 100