There are 22 full-time employees at the shop. New employees receive $9.50 per hour, while experienced workers average $12.90 per hour. The company spends $273.60 per hour in wages. Find the number of each type of worker.

The 22 employees are made up of new employees and experienced employees. If we use x to denote the number of new employees and y to denote the number of experienced employees, then

x + y = 22 because 22 is the total number of employees.

The company spends 9.50x on the new employees and spends 12.90y on the experienced employees, so

9.50x + 12.90y = 273.60 because $273.60 is the total the company spends on wages.

Now let's solve these two equations to find out how many new employees and experienced employees are working.

From the first equation, multiplying each side by 9.50, we get

9.50x + 9.50y = 22*9.50

If we subtract this from the second equation the 9.50x term cancels and we get

3.40y = 273.60 - 22*9.50 = 64.60

So y = 64.60/3.40 = 19 - there are 19 experienced employees

And so there are 22-19 = 3 new employees.