Answer: the lowest commission is $163.96
Step-by-step explanation:
Let x represent the lowest monthly commission that a salesman earned.
Let y represent the highest monthly commission that a salesman earned.
The lowest monthly commission that a salesman earned was only 1/5 more than 1/4 as high as the highest commission he earned. This means that
x = y/4 + 1/5 - - - - - - - - 1
The highest and lowest commissions when added together equal $819. This means that
x + y = 819
x = 819 - y - - - - - - -2
Substituting equation 2 into 1, it becomes
819 - y = y/4 + 1/5
Multiplying through by 20, it becomes
16380 - 20y = 5y + 4
25y = 16380 - 4 = 16376
y = 16376/25 = 655.04
x = 819 - 655.04 = 163.96
