Question

A sales person is given a choice of two salary plans. plan 1 is a weekly salary of 500 plus 3% commission of sales. plan 2 is a straight commission of 5% of sales. how much in sales must she make in a week for both plans to result in the same salary

Answer 1

Let's write and equation for both cases.

In plan 1, it is 500 plus 3% comission. 3% is equivalent to multiply the amount it sale in the week, "x", by 0.03.

So, the equation for plan 1 is:

`p_1=0.03x+500`

For plan 2, there is no fixed value, only comission of 5%, which is equivalent of multiplying the weekly sales, "x", by 0.05, so the equation is:

`p_2=0.05x`

For both plans to result in the same salary, we have:

`\begin{gathered} p_1=p_2 \\ 0.03x+500=0.05x \\ 0.05x-0.03x=500 \\ 0.02x=500 \\ x=(500)/(0.02) \\ x=25,000 \end{gathered}`

So, for both plans to result in the same salary, she have to sale 25,000 in a week.