Question

At one company a level 1 engineer receives a salary of $45,000 and a level 2 receives a salary of $65,000. The company has a budget of $785,000 to pay for both levels. Also, they can afford to hire 13 engineers from level 1 and level 2. How many engineers should be hired for each level ?

Answer 1

Company will hire 3 Engineers of Level 1 and 10 Engineers of level 2.

Explanation:

Let the number of engineers for level 1 be x.

Let the number of engineers for level 2 be y.

Given:

Total Number of engineers company can hire = 13

Now Total number of engineers are equal to sum of number of engineers for level 1 and number of engineers for level 2.

Hence Framing in the equation form we get;

`x+y=13 \ \ \ \ equation\ 1`

Also Given:

Salary of level 1 engineers = $45,000

Salary of level 2 engineers = $65,000

Total Budget of Company = $785,000

But Total Budget of Company depends upon the sum of Salary of level 1 engineers multiplied with number of level 1 engineers and Salary of level 2 engineers multiplied with number of level 2 engineers.

Hence equation can be framed as;

`45000x+65000y = 785000`

Dividing by 5000 on both side we get;

`(45000x)/(5000)+(65000y)/(5000)=(785000)/(5000)\\\\9x+13y=157 \ \ \ \ equation\ 2`

Now Multiplying equation 1 by 9 we get;

`9(x+y)=13*9\\9x+9y= 117 \ \ \ \ equation\ 3`

Now Subtracting equation 3 from equation 2 we get;

`(9x+13y)-(9x-9y)=157-117\\\\9x+13y-9x-9y=40\\\\4y=40\\\\y=(40)/(4) =10`

Now Substituting the value of y in equation 1 we get

`x+y=13\\x+10=13\\x=13-10\\x=3`

Hence Company will hire 3 Engineers of Level 1 and 10 Engineers of level 2.