We are asked to determine which renting scheme gives a better value.
The cost per day is equal to the fixed fee per day plus the cost per mile by the number of miles. Therefore, Rent-A-Hunk's cost is given by:
[tex]C=29.95+0.43x[/tex]
Where "x" is the number of miles.
For Tom's total wrecks we have:
[tex]C=45+0.32x[/tex]
The graphs of both costs is the following:
Therefore, Rent-A-Hunk gives a better price until we get to the interception point I. Therefore, we need to determine the value of "x" where both graphs intercept. To do that we set both equations equal:
[tex]29.95+0.43x=45+0.32x[/tex]
Now, we solve for "x". To do that we subtract "0.32x" from both sides:
[tex]\begin{gathered} 29.95+0.43x-0.32x=45+0.32x-0.32x \\ 29.95+0.11x=45 \end{gathered}[/tex]
Now, we subtract 29.95 from both sides:
[tex]\begin{gathered} 0.11x=45-29.95 \\ 0.11x=15.05 \end{gathered}[/tex]
Now, we divide both sides by 0.11:
[tex]x=\frac{15.05}{0.11}[/tex]
Now, we solve the operation:
[tex]x=136.8[/tex]
Therefore, the interception point is 136.8 miles.
This means that Rent-A-Hunk is a better price if the number of miles per day is less than 136.8 and Tom's Total Wrecks is better if the number of miles per day is greater than 136.8 miles.
If the number of miles is 136.8 then both values are the same.
