Question

A salesperson makes a base salary of $15,000 per year plus a 8% commission on total sales for the year. The yearly salary can be expressed as a linear function.

Answer 1

The salary of the salesperson can be represented as "y" and the number of sales for the year will be represnted as "x". With this in mind the salary will be the fixed part (15000) plus the number of sales per year multiplied by 8 percent. With this in mind we have:

`\begin{gathered} y(x)=15000+8\text{\%}\cdot x \\ y(x)=15000+(8)/(100)\cdot x \\ y(x)=15000+0.08\cdot x \end{gathered}`

The function that represents his yearly salary is "y(x)=15000+0.08*x".

To find his salary when he sells $500,000 in a year we need to make x equal to that value. Therefore:

`\begin{gathered} y(500000)=15000+0.08\cdot500000 \\ y(500000)=15000+40000 \\ y(500000)=55000 \end{gathered}`

His salary will be $55,000 for that year.