SOLUTION: I'm trying to solve this word problem, but I don't think I'm getting the inequality equation right. Can you help me? Greg can rent a van for either $50 per day with unlimited m

Question 55657: I'm trying to solve this word problem, but I don't think I'm getting the inequality equation right. Can you help me?
Greg can rent a van for either $50 per day with unlimited mileage or $35 per day with 75 free miles and an extra charge of $.25 for each mile over 75. For what numbers of miles traveled would the unlimited mileage plan save Greg money?

I've tried:
50x>35+.25(x-75), 50x>35+.25x, 50x>35+25(x-75)...I don't think the solutions I'm getting with these are right. Please help!
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
I'm trying to solve this word problem, but I don't think I'm getting the inequality equation right. Can you help me?
Greg can rent a van for either $50 per day with unlimited mileage or $35 per day with 75 free miles and an extra charge of $.25 for each mile over 75. For what numbers of miles traveled would the unlimited mileage plan save Greg money?
`
I've tried:
50x>35+.25(x-75), 50x>35+.25x, 50x>35+25(x-75)...I don't think the solutions I'm getting with these are right. Please help!
`
Your first error is that the 50x should be just 50. It's a flat rate of $50, you don't need to multiply it by anything. You're trying to multiply it by the number of miles. Just leave it 50. Also you have the inequality the wrong way. We want the 50 to be the cheaper, so we want it to be less than the right side, not greater. Then your inequality is just
`
50 < 35 + .25(x - 75) (where, of course, x > 75)
`
Solve this and you get 135 < x which may be written x > 135
`
Edwin

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