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Felipe will rent a car for the weekend. He can choose one of two plans.The first plan has an initial fee of $55 and costs an additional $0.10 per mile down. The

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3 Answers

Hey Angela, the simplest way to do this problem is setting both sides equal to each other.  You'll have 55 + .1x = .6x.  You can do this with virtually any "when will plan A be equal to plan B" type of problem.  Now, as we have our equation, let's solve for x; 55 = .6x - .1x => 55 = .5x.  Next, we divide 55/.5 = 110 = x.  Therefore, at 110 miles, the plans will be the same.

 

Another example of this would be say plan A is $45 down and $0.10 per mile, plan B is $65 down and $.05 a mile.  Which plan would be better if you were driving 50 miles.

Setting this up in the same way, we get 45 + .10x = 65 + .05x.  Combine like terms, and we get .05x = 20.  Dividing, we'll get x = 400 miles is where they're equal, with the Plan A better for short periods and plan B better for longer periods (lower slope).

Hey Angela -- if Felipe is going to drive a lot of miles, pay the fixed fee with the lower-mileage rate. Driving a few miles is better with the "no-fee" plan and higher-mileage rate. There is a certain number of miles where the cost is the same: 1st plan at 110 miles costs $55 + $11 or $66; 2nd plan at 60 cents/mile costs $66, too.   

Angela - I think you need to re-enter your question with a shorter title. This entry has cut off; all I can see of the question is "Felipe will rent a car for the weekend. He can choose one of two plans.The first plan has an initial fee of $55 and costs an additional $0.10 per mile down. The"