A company hires skilled employees, each working under contract to 35h and paid € 550 a week, others working under contract B 20h and paid € 220 per week.

Question

A company hires skilled employees, each working under contract to 35h and paid € 550 a week, others working under contract B 20h and paid € 220 per week.

1. These employees will have to make a total of 370h of work per week and the entrepreneur has a Bugdet weekly € 5,060 to pay them. How should it hire employees under contract A and B contract employees? (use linear equation system 2)

Answer 1

To find out how many employees should be hired under contract A and contract B, we can set up a system of linear equations based on the given information.

Let's assume the number of employees hired under contract A is 'x' and the number of employees hired under contract B is 'y'.

From the given information, we have the following equations:

1. Total working hours equation:
The total working hours should be 370 per week. So, for the employees under contract A, each working 35 hours, we get 'x' multiplied by 35. And for the employees under contract B, each working 20 hours, we get 'y' multiplied by 20.
Therefore, the equation is:
35x + 20y = 370

2. Total budget equation:
The total budget available to pay the employees is €5,060 per week. So, for the employees under contract A, each paid €550, we get 'x' multiplied by 550. And for the employees under contract B, each paid €220, we get 'y' multiplied by 220.
Therefore, the equation is:
550x + 220y = 5060

Now, we have a system of linear equations to solve:
35x + 20y = 370
550x + 220y = 5060

We can solve this system using any method of solving linear equations, like substitution or elimination. Let's solve it using the elimination method.

First, we can multiply the first equation by 11 to make the coefficients of 'y' the same, so we can eliminate 'y'.

Multiplying the first equation by 11, we get:
385x + 220y = 4070

Now, subtracting the second equation from this new equation, we get:
(385x + 220y) - (550x + 220y) = 4070 - 5060
385x - 550x = -990
-165x = -990

Dividing both sides by -165, we get:
x = (-990) / (-165)
x = 6

Substituting the value of 'x' back into one of the original equations (let's use the first equation), we can solve for 'y'.

35(6) + 20y = 370
210 + 20y = 370
20y = 370 - 210
20y = 160
y = 160 / 20
y = 8

Therefore, the company should hire 6 employees under contract A and 8 employees under contract B to meet the given requirements.