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}* s) \\ \text{ \$700+(0.04}* s)=\text{ \$700}+0.04s \end{gathered}`

Plan 2:

`12\text{ \% of s}`
`\begin{gathered} (12)/(100)* s \\ 0.12* 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} (0.08s)/(0.08)=\frac{\text{ \$700}}{0.08} \\ s=\text{ \$8750} \end{gathered}`

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