Question

Teresa is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices: company A charges an initial fee of $58 and an additional 40 cents for every mile driven. Company B charges an initial fee of $40 and an additional 69 cents for every mile driven. For what mileages will company A charge no more than company B? Write your answer as an inequality, using m for the number of miles driven.

Answer 1

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:

`0.4* x\text{ dollars}`

Therefore, in total, Teresa will be charged by company A the following:

`(58+0.4x)\text{dollars}`

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:

`0.69* x\text{ dollars}`

Therefore, in total, Teresa will be charged by company B the following:

`(40+0.69x)\text{dollars}`

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:

`(58+0.4x)\text{dollars }\leq(40+0.69x)\text{dollars}`

Thus, we simply the above and solve for x, as follows:

`58+0.4x\leq40+0.69x`

Collect like terms:

`\begin{gathered} 0.4x-0.69x\leq40-58 \\ \Rightarrow-0.29x\leq-18 \end{gathered}`
`\begin{gathered} \Rightarrow x\ge(-18)/(-0.29)\ge62.07 \\ \Rightarrow x\ge62\text{ miles} \end{gathered}`