An employee earns $20 for each day he works, and he forfeits $4.00 for each day that he is idle. if at the end of 40 days, the employee earns $656, how many days was he idle?

6 days

Explanation:

Let days worked = x

Let days idle = y

x + y = 40

20x - 4x = 656

Lets choose a variable to eliminate (We'll choose y)

(x + y = 40) 4

20x - 4y = 656

Distribute

4x + 4y = 160

20x - 4y = 656

The -4y cancels out the 4y and then we combine

24x = 816

Divide both sides by 24

24x/24 = 816/24

x = 34

Active days = 34

40 days - 34 active days = 6 idle days

he was idle for 6 days

Explanation:

Let x represent the number of days that the employee works.

Let y represent the number of days that the employee is idle.

If he works for 40 days, it means that

x + y = 40

An employee earns $20 for each day he works, and he forfeits $4.00 for each day that he is idle. If at the end of 40 days, the employee earns $656, it means that

20x - 4y = 656 - - - - - - - - - - 1

Substituting x = 40 - y into equation 1, it becomes

20(40 - y) - 4y = 656

800 - 20y - 4y = 656

- 20y - 4y = 656 - 800

- 24y = - 144

y = - 144/ -24

y = 6

Substituting y = 6 into x = 40 - y, it becomes

x = 40 - 6 = 34