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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.

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Kenneth G. | Experienced Tutor of Mathematics and StatisticsExperienced Tutor of Mathematics and Sta...
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.
Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (189 lesson ratings) (189)
Let Nn=the number of new employees @$9.50/hr
Let Ne=the number of experienced employees@$12.90/hr
So we know that 1) Nn+Ne=22 and 2) 9.5xNn + 12.9xNe=273.6. so now you have 2 equations with 2 unknowns. So you can solve say equation 1) for Ne=22-Nn and sub this into equation 2) and solve for Nn.Then put this back in equation 1) and solve for Ne
You should get Nn=3 and Ne=19 
Hope this helps
Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
5.0 5.0 (260 lesson ratings) (260)

Let x be the number of new employees.

Let y be the number of experienced employees.

Total employees at the shop = 22
Therefore, x+y=22 (given in the question)
                x=22-y (equation 1)
New employees receive $9.50 per hour , while experience workers receive $12.90 per hour.
So total of all new employees receive wages =9.50x, while total of all experience employees receive wages=12.90y
The company pays total wages = $273.60 (given in the question)
The statement using x and y values will be:
Substitute value of x from equation 1
9.50 (22-y)+12.90y = 273.60
202.50 - 9.50y + 12.90y = 273.60
202.50 + 3.4y = 273.60
3.4y = 273.60-202.50
y = 64.60/3.4
y = 19    (equation 2)
Solve for equation 1, using value of y from equation 2:
x = 22-y
x = 22-19
x = 3
Therefore number of new employees are 3 and experienced employees are 19.
Hope this helps you to understand the question better.
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
let x=# of employees earning $9.50 per hour
let y=# of employees earning $12.90 per hour
x+y=22 so x=22-y
substitute x=22-y into 9.5x+12.9y=273.6
y=19 employees earning $12.90 per hour
22-19=3 employees earning $9.50 per hour