We have the following parameter
Company A
The charges is given by
[tex]\begin{gathered} \text{ 120 + }0.8x \\ \text{where x is the number of miles} \end{gathered}[/tex]
Company B
The charges is given by
[tex]60+0.9x[/tex]
To determine how many miles it will take for the rental cost of company A to exceed B, we will set up the inequality
[tex]120+0.8x<60+0.9x[/tex]
To find the number of miles, we will make x the subject of the formula
[tex]\begin{gathered} 120-60<0.9x-0.8x \\ 60<0.1x \end{gathered}[/tex]
Re-arranging
[tex]\begin{gathered} 0.1x>60 \\ x>\frac{60}{0.1} \\ x>600\text{ miles} \end{gathered}[/tex]
Therefore, for the rental cost of company A to be better than company B, the number of miles driven in a day must be greater than 600 miles
