Carcass wrote:

Employee X is paid $ 19.50 an hour no matter how many hours he works per week. Employee Y is paid $ 18 an hour for the first 40 hours she works in a week and is paid 1.5 times the hourly rate for every additional hour she works. On a certain week, both employees worked the same number of hours and were paid the same amount. How many hours did each employee work that week?

A. 32

B. 36

C. 40

D. 42

E. 48

Kudos for the right answer and explanation

The equations that describe the pay for the employees are:

y = 19.50*(40 + x)

y = 18*40 + (18*1.5)*x = 18*40 + 27 *x

note that 40 represents the number of hours already worked (since we know at least that much time must have passed)

and then x represents the number of hours over 40 that need to be worked before their pays intersect.

Now set them equal and solve

19.50*(40 + x) = 18*40 + 27 *x

780 + 19.5*x = 720 + 27 * x

60 = 7.5x

x = 8

40 (hours already worked ) + 8 = 48