SOLUTION: Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra $.25 for each mile over 250. for what number of miles traveled in o

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Question 1182609: Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra $.25 for each mile over 250. for what number of miles traveled in one day with the unlimited mileage plan save Lia money?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
unlimited plan is 90 dollars a day with no additional mileage charge.

alternate plan is 50 dollars a day with 250 free miles and an extra .25 per mile for any miles above 250.

the unlimited plan will save money if the alternate plan costs more than 90 dollars total.

alternate plan starts at 50 dollars with 250 unlimited miles.
any miles over 250 are charge at .25 per mile.

alternate plan equation is y = 50 + .25 * (x - 250) where x > 250
this is compare to 90 dollars for the limited plan.

replace y with 90 to get:

90 = 50 + .25 * (x - 250)
subtract 50 from both sides of the equation to get:
40 = .25 * (x - 250)
divide both sides of the equation by .25 to get:
40/.25 = x - 250
simplify to get:
160 = x - 250
add 250 to both sides of the equation to get:
x = 410

they should break even when the alternate plan travels 410 miles.
the cost for the alternate plan would be 50 dollars + .25 * (410 - 250) = 50 + .25 * 160 = 50 + 40 = 90.

any miles traveled over 410 miles in the alternate plan will make it more expensive than the unlimited plan.

you can see this from the following graph.



red is the unlimited plan.
blue is the alternate plan.
coordinate points are in (x,y) format.
x is the number of miles driven.
y is the total cost.

unlimited plan cost 90 dollars.
alternate plan costs 50 dollars when 250 miles have traveled and 90 dollars when 410 miles have traveled.

anything over 410 miles and the unlimited plan comes out the winner.