Question

In the following exercises, translate to a system of equations and solve.

Jackie has been offered positions by two cable companies. The first company pays a salary of \( 14,000 plus a commission of \)100 for each cable package sold. The second pays a salary of \(20,000 plus a commission of \)25 for each cable package sold. How many cable packages would need to be sold to make the total pay the same?

Short answer

The number of cable packages need to sell is 80.

Step-by-step solution

Step 1. Given Information   

The given data is that the first company pays a salary of $ 14,000 plus a commission of $100 for each cable package sold. The second pays a salary of $20,000 plus a commission of $25 for each cable package sold.

Step 2. Calculation 

Let us assume that xbe the number of cable packages need to be sold.

As the first company pays a salary of $ 14,000 plus a commission of $100 for each cable package sold. The second pays a salary of $20,000 plus a commission of $25 for each cable package sold. This will make the equation as follows,

$14000+100\left(x\right)=20000+25\left(x\right)$

Solve the equation to find the value of variablex.

$$\begin{gathered} 14000+100x=20000+25x \\ 75x=6000 \\ x=80 \end{gathered}$$