How many full-time and part-time employees can be hired?

Question

They set a budget of $1,225,000 to pay them every year, knowing that people employed full time will received an annual salary of $35,000 and half time people will receive $17,500 per year. A town regulation states that the number of half-time employees needs to be half the number of full-time employees.

 

 

Each employee works 6 days of the week and rests one. How many full-time and half-time employees work each day and how many rest? Remember, each day the town regulation remains.

Answer 1

let x = # of full time employees and x/2 = # of half-time employees

 

then x•$35,000 + x/2•$17,500 = $1,225,000

$43,750x + $8,750x = $1,225,000

x = 28 then x/2 = 14

 

Proof: 28•$35,000 + 14•$17,500 = $1,225,000

$980,000 + $245,000 = $1,225,000

Answer 2

 

Let F = number of full-time employees

Let H = number of half-time employees

 

   F = 2H

 

   35,000F + 17500H = 1,225,000

 

Using substitution

 

   35,000(2H) + 17,500H = 1,225,000

 

   70,000H + 17,500H = 1,225,000

   

   87,500H = 1,225,000

 

   H = 1,225,000/87,500

 

   H = 14

 

They need to hire 14 half-time employees and 28 fulll-time employees.

Answer 3

Karla,

 

We can use a system of equations to solve this.

 

First, let 'x' represent the number of full-time employees and 'y' represent the number of half-time employees.

 

Then, we know a couple things.

 

(1) y = 1/2x (the number of half-time employees is equal to 1/2 the number of full-time employees.

 

We also know that:

 

(2) $35,000x + $17,500y = $1,225,000 (total salary in the budget is equal to the sum of the full-time and half-time salaries)

 

Now, substitute the value for y (1/2x) in eq1 for 'y' in eq2:

 

$35,000x + $17,500(1/2x) = $1,225,000

 

$35,000x + $8,750x = $1,225,000

 

$43,750x = $1,225,000

 

$43,750x/$43,750 = $1,225,000/$43,750

 

x = 28 full-time employees

 

To find the number of half-time employees, remember that:

 

y = 1/2x => y = 1/2 * 28 => y = 14 half-time employees.

 

Hope this helps.

Answer 4

Let x = # full time and y=# part time, set up a system of 2 equation sin 2 variables

 

35000x + 17500y = 1225000

 

x = 2y  and solve via substitution

 

35000(2y) + 17500y = 1225000

 

87500y = 1225000

 

y=14, x = 28