Respuesta :
Let x represent the number of miles driven by both individuals.
Now, since COMPANY A will charge Teresa an initial constant fee of $58 and then an additional 40 cents (or $0.4) for every mile driven, we know that:
- if Teresa drives x miles, she will be charged:
[tex]0.4\times x\text{ dollars}[/tex]Therefore, in total, Teresa will be charged by company A the following:
[tex](58+0.4x)\text{dollars}[/tex]Also, since COMPANY B will charge Teresa an initial constant fee of $40 and then an additional 69 cents (or $0.69) for every mile driven, we know that:
- if Teresa drives x miles, she will be charged:
[tex]0.69\times x\text{ dollars}[/tex]Therefore, in total, Teresa will be charged by company B the following:
[tex](40+0.69x)\text{dollars}[/tex]Now, the milieage (x) for which both companies A will charge Teresa no more than company does is obtained by relating the expressions for their separate fees as follows:
[tex](58+0.4x)\text{dollars }\leq(40+0.69x)\text{dollars}[/tex]Thus, we simply the above and solve for x, as follows:
[tex]58+0.4x\leq40+0.69x[/tex]Collect like terms:
[tex]\begin{gathered} 0.4x-0.69x\leq40-58 \\ \Rightarrow-0.29x\leq-18 \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow x\ge\frac{-18}{-0.29}\ge62.07 \\ \Rightarrow x\ge62\text{ miles} \end{gathered}[/tex]