SOLUTION: Please help with this problem, I can't seem to get it set up right, Thanks in advance. John and Sherry needed to rent a car for a week.Avis wanted $28 per day, with no mileage fee

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Question 104253: Please help with this problem, I can't seem to get it set up right, Thanks in advance.
John and Sherry needed to rent a car for a week.Avis wanted $28 per day, with no mileage fee. Toyota wanted $108 per week and $.14 per mile. How many miles would they have to drive before the Avis price is less than the Toyota price?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's find an equation for each car rental.
A+=+28%2AD
T+=+108%2AW%2B0.14%2AM
Since there is a difference between the days equation and the weeks equation. Let's change the first one to be on a week basis also. Since there are 7 days in a week, we multiply by 7.
A=7%2A28%2AW
A=196W
Let's find out when Avis and Toyota would be the same price.
A=T
196W=108W%2B0.14%2AM
196W-108W=0.14%2AM
88W%2F0.14=M
629W=M
So if you drive 629 miles in one week. Avis and Toyota will have the same price for the rental. If you drive more than 629 miles in a week, Toyota will have the higher price. In other words, your mileage rate where you start to pay more is 629 miles/week. This gets you around not knowing how many days you have the rental.
Check your answer.
Let's say you drove 1500 miles in two weeks.
Since 1500 miles > 2 weeks*629 miles/week (1258 miles), you would expect Toyota to be higher in cost.
Avis would charge you :
A=28%2A14=392
Avis' charge is $392.
Toyota would charge you :
T=108%2A2%2B0.14%2A1500=206
Toyota's charge is $426.
Toyota is $34 more than Avis, as you expected.