Explanation:
We will have to get the equations
Plan X
Let the number of weekly sales be represented by d
So the equation will be
[tex]\begin{gathered} =1000+10\text{\% of d} \\ =1000+0.1d \end{gathered}[/tex]
For plan Y
We will have
[tex]\begin{gathered} =500+20\text{\% of d} \\ =500+0.2d \end{gathered}[/tex]
The question wants us to determine when salespeople on plan X will earn more than on plan Y
We will set up the inequality
[tex]\begin{gathered} X>Y \\ =1000+0.1d>500+0.2d \\ =1000-500>0.2d-0.1d \\ =500>0.1d \end{gathered}[/tex]
Re-writing this, we will have
[tex]\begin{gathered} 0.1d<500 \\ dividing\text{ both sides by 0.1} \\ \frac{0.1d}{0.1}<\frac{500}{0.1} \\ d<5000 \end{gathered}[/tex]
Therefore, the answer is d< 5000
