# Labor Day: salary with commission helps to understand related function

Mathematics sometimes seems very distant from “real life”. But it is just the opposite: it is present in “normal” moments of our lives, without us even realizing it.

This is the case with sellers who work on commission. Everyone in this situation knows very well how to calculate the salary at the end of the month, but few people give a “difficult name” for this account: first degree function.

## First degree function

The first-rank function, or related function, is one that has only one variable. This means that it only has “x” – and without being raised to anything.

This is the case of those who work with commission. The person has a fixed salary, which receives even if he does not sell anything. And in addition to that, you can earn more by making more sales.

The commission is usually calculated from a percentage. That is, this account requires percentage as well as function. Let’s see the step by step?

### Who is the variable?

If we think only of “real life,” without mathematics, we can understand. What varies (the variable) in the salary of that salesperson? The commission.

To assemble the function, then, we have the non-changing part (the wage) and the part that varies (variable):

base salary + commission = paycheck of the month

### Percentage commission

Well, if the salary is always the same, it remains to know the commission, right? We have already seen that it is a percentage, that is, a number on (divided by) 100.

Let’s say, then, that the commission is 5% per piece sold. Thus we will have:

part value * 5% = part value * 5/100 = total commission for the month

It is clear, then, that the value of the commission will depend on the price of the parts sold throughout the month (since the salary is monthly). And, everyone who works knows, the more you sell, the more the professional will earn by the end of the month.

Now that we understand what happens in “real life,” let’s go to mathematics? She was there all the time, except we were not calling her.

In the first degree function, as we have already seen, we have a fixed and a variable term. Now, we already know that the fixed is the base salary, and the variable is the commission.

To assemble the mathematical formula, simply replace the words with letters:

a + x = y

Oh, it’s complicated? Let’s take it easy: “a” is the salary, which is always the same. The “x” is the variable, that is, the commission, that each month will be different. And “y” is the money in Angela’s account every fifth helpful of the month. And we can complicate more:

a + 5z / 100 = y

In this case, 5/100 represents the 5% commission. The “z” now is not the final commission (the \$ 100 we calculated earlier), but the total value of sales, on which it would still be necessary to calculate the commission.

If you’re a star, you may have noticed that 5/100 can be simplified. Both are multiples of 5, so you can write:

a + z / 20 = y

Now, yes, huh! Can you explain this equation to Angela? Test with the exercises in this link! Remember: if an account looks difficult, maybe using a real-life example makes “x”, “y”, “a” and “b” easier!