Question

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

Amara currently sells televisions for company A at a salary of \(17,000 plus a \)100 commission for each television she sells. Company B offers her a position with a salary of \(29,000 plus a \)20 commission for each television she sells. How televisions would Amara need to sell for the options to be equal?

Short answer

The number of television need to sell is 150.

Step-by-step solution

Step 1. Given Information 

The given data is that she sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells.

Step 2. Calculation 

Let us assume that xbe the number of televisions need to sell.

As she sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells.

This will give the equation as follows,

$17000+100\left(x\right)=29000+20\left(x\right)$

Solve the equation to find the value of variable x.

$$\begin{gathered} 17000+100x=29000+20x \\ 80x=12000 \\ x=150 \end{gathered}$$