Chris can be paid in one of two ways. Plan A is a salary of $450 per month, plus a commission of 8% of sales. Plan B is a salary of$695 per month, plus of 3% of sales. For what amount of sales is Chris better off selecting plan A?

Jan 8, 2017

See full explanation below.

Explanation:

First, when dealing with percents, "Percent" or "%" means "out of 100" or "per 100", Therefore x% can be written as $\frac{x}{100}$.

The expression for Plan A can be written as:

$450 + \frac{8}{100} s$ where $s$ is the sales for the month.

The expression for Plan B can be written as:

$695 + \frac{3}{100} s$

The question we are being asked is when is Plan A > Plan B. So, we can write and solve this inequality:

$450 + \frac{8}{100} s > 695 + \frac{3}{100} s$

$450 + \frac{8}{100} s - \textcolor{red}{450} - \textcolor{b l u e}{\frac{3}{100} s} > 695 + \frac{3}{100} s - \textcolor{red}{450} - \textcolor{b l u e}{\frac{3}{100} s}$

$450 - \textcolor{red}{450} + \frac{8}{100} s - \textcolor{b l u e}{\frac{3}{100} s} > 695 - \textcolor{red}{450} + \frac{3}{100} s - \textcolor{b l u e}{\frac{3}{100} s}$

$0 + \frac{8}{100} s - \textcolor{b l u e}{\frac{3}{100} s} > 695 - \textcolor{red}{450} + 0$

$\frac{8}{100} s - \textcolor{b l u e}{\frac{3}{100} s} > 695 - \textcolor{red}{450}$

$\left(\frac{8}{100} - \textcolor{b l u e}{\frac{3}{100}}\right) s > 245$

$\frac{5}{100} s > 245$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{5}} \times \frac{5}{100} s > \frac{\textcolor{red}{100}}{\textcolor{b l u e}{5}} \times 245$

$\frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{5}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{5}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} s > \frac{24500}{\textcolor{b l u e}{5}}$

$s > 4900$

Plan A is better when sales for the month are greater than \$4,900.