Question

A sales person is given a choice of two salary plans. Plan 1 is a weekly salary of 700 plus 4% commission of sales. Plan 2 is a straight commission of 12%Of sales. How much in sales must he make in a week for both plans to result in the same salary?

Answer 1

Let 's' represent the amount of sales.

Plan 1:

$\text{ \ 700 + (4\% of s)}$$\begin{gathered} \text{ \ 700+(}\frac{\text{4}}{100}\times s) \\ \text{ \ 700+(0.04}\times s)=\text{ \ 700}+0.04s \end{gathered}$

Plan 2:

$12\text{ \% of s}$$\begin{gathered} \frac{12}{100}\times s \\ 0.12\times s=0.12s \end{gathered}$

Equating the two plans together and solving for the amount of sales,

$\begin{gathered} \text{Plan 2=Plan 1} \\ 0.12s=\text{ \ 700+0.04s} \\ \end{gathered}$

Collecting like terms,

$\begin{gathered} 0.12s-0.04s=\text{ \ 700} \\ 0.08s=\text{\ 700} \end{gathered}$

Divide both sides by 0.08,

$\begin{gathered} \frac{0.08s}{0.08}=\frac{\text{ \ 700}}{0.08} \\ s=\text{ \ 8750} \end{gathered}$

Hence, the amount of sales is $8,750.