Q. 4.29 - Intermediate Algebra

Question

Geraldine has been offered positions by two insurance companies. The first company pays a salary of \(12,000 plus

a commission of \)100 for each policy sold. The second pays a salary of \(20,000 plus a commission of \)50 for each

policy sold. How many policies would need to be sold to make the total pay the same?

Step-by-Step Solution

Answer

If Geraldine sells $160$ policies than he will make the total pay same.

Step 1. Given data and Forming equation

On reading the problem we can see that there are two variable which are Unknown salary and number of policy.

s = Geraldine’s salary.

n = the number of policies sold.

Using the given data we will write the equation.

The first company pays a salary of $$12,000$ plus a commission of $$100$ for each policy sold so the equation is:

$S=12,000+100n.....\left(1\right)$

The second pays a salary of $$20,000$plus a commission of $$50$ for each policy sold, so the equation is:

$s=20,000+50n....\left(2\right)$

Step 2. Solving equation

We can solve both the equation$n$ as both the salary will be equal for given $n$

$\begin{array}{rcl}12,000+100n& =& 20,000+50n\\ 50n& =& 8000\\ n& =& 160\end{array}$

 He will need to sell $160$ policies to make them pay the same.