Answer/Step-by-step explanation:
Equation to represent the daily rental cost for each type of truck can be written as follows:
Daily rental cost for Trucks-A-Lot = 42 + 0.72m
Daily rental cost for Move-in-Truckers = 70 + 0.12m
Where, m = Emily's mileage
To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.
![42 + 0.72m = 70 + 0.12m](https://tex.z-dn.net/?f=%2042%20%2B%200.72m%20%3D%2070%20%2B%200.12m%20)
Collect like terms
![0.72m - 0.12m = 70 - 42](https://tex.z-dn.net/?f=%200.72m%20-%200.12m%20%3D%2070%20-%2042%20)
![0.6m = 28](https://tex.z-dn.net/?f=%200.6m%20%3D%2028%20)
Divide both sides by 0.6
![\frac{0.6m}{0.6} = \frac{28}{0.6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.6m%7D%7B0.6%7D%20%3D%20%5Cfrac%7B28%7D%7B0.6%7D%20)
![m = 46.7](https://tex.z-dn.net/?f=%20m%20%3D%2046.7%20)
At approximately 47 miles, both trucks would cost the same amount.
Check:
Daily rental cost for Trucks-A-Lot = 42 + 0.72m
Plug in the value of x = 47
= 42 + 0.72(47) = $75.84 ≈ $76
Daily rental cost for Move-in-Truckers = 70 + 0.12m
Plug in the value of x = 47
= 70 + 0.12(47) = $75.64 ≈ $76