Question

It takes 20 hours and $400 to interview a candidate, and it takes 120 hours and $3600 to train an employee.

A company has less than $95000 to interview and train employees, and it wants to spend at most 470 hours to do so.


Let C denote the number of candidates they interview and E the number of employees they train


Write an inequality that represents the condition based on the number of dollars the company can spend.


Write an inequality that represents the condition based on the number of hours the company wants to spend.

Answer 1

400C+3600E<95000
-
20C+120E≤470

Explanation:

It was right on khan

Answer 2

`400x+3600y<95000\\ 20x+120y\leq 470`

Explanation:

The first thing we need to do is to identify the characteristics of this problem. As you can see, this situation has restriction, limitations on how much money and time they can spend.

In mathematics, restrictions are expressed with inequalities, because it gives us the power to express in terms of more or less than something. When we have this inequality-restrictions problems, it's very helpful to organise all info, so according to the problem, we have:

$ hr

Candidates (x) 400 20

Employees (y) 3600 120

Max. 95000 470

We this organisation, we can easily find expressions, the important thing here is to put together similar variables, money with money and time with time.

So, you can see that, the maximum money they can spend is 95000, and the maximum time is 470 hours, which give us:

`400x+3600y<95000\\ 20x+120y\leq 470`

As you can see, for money inequality, we used < (less than), and for hours we used ''less or equal than''. This difference is because in the text it says that they has less than 95000 (not equal than 95000), and for hours they have at most 470 (meaning that this is a maximum, 470 and below that number).

Therefore, those two inequality express the restriction about money and time limitations for candidates and employees.