Question 1190430: OMG I need help! I cannot solve this problem for the life of me. Please explain so I can understand. I think the unlimited miles is what's messing me up. Thanks in advance!
A car rental company offers 2 plans for renting a car
Plan A: $40 per day and $0.19 per mile
Plan B: $60 per day with unlimited miles
For what range of miles will Plan B save you money for a 1 day rental?
For what range of miles will Plan A save you money for a 1 day rental?
Give your answer accurate to at least one decimal place.
Found 3 solutions by math_tutor2020, Theo, greenestamps:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The "unlimited" miles means that the company doesn't charge per mile in this scenario. All they get is the $60 per day.
If you only rent for one day, then all they get is the $60. This applies to plan B only of course.
x = number of miles
y = total cost
If you only plan to do a 1 day rental, then,
Plan A has the equation y = 0.19x+40
The 0.19x is the extra 19 cents (aka $0.19) per mile on top of the $40 initially paid
Plan B has the equation y = 60 for 1 day rentals.
The x is not involved because again they don't charge per mile. The cost is simply 60 dollars.
Both cost equations involve y
Let's apply substitution to find x
y = 60
0.19x+40 = 60 ... y replaced with 0.19x+40
0.19x = 60-40
0.19x = 20
x = 20/0.19
x = 105.263 approximately
This rounds to 105.3 when rounding to one decimal place.
The two costs are roughly the same when driving 105.3 miles for 1 day rentals.
If you traveled 105 miles in one day, then plan A costs you
y = 0.19x+40
y = 0.19*105+40
y = 19.95+40
y = 59.95
which is just barely under the $60 mark. This shows that plan A is the better choice for this mileage.
If you traveled 106 miles in one day, then plan A costs you
y = 0.19x+40
y = 0.19*106+40
y = 20.14+40
y = 60.14
You are paying 14 cents more than if you went with plan B.
For any larger x values, plan A will get more expensive and it's better to go for plan B.
Intuitively this is what we'd expect because plan A's cost grows based on the number of miles driven, while B has a fixed cost.
Those are two examples to show that the boundary is 105.3
I'll let you play with other x values. I recommend making a table to compare costs.
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Answers:
For what range of miles will Plan B save you money for a 1 day rental? Anything larger than 105.3 miles
For what range of miles will Plan A save you money for a 1 day rental? Anything between 0 and 105.3 miles
In terms of inequalities, the first statement in red is the same as saying  while the second statement would translate to  , where x is the number of miles driven. Also, this all applies to one day rentals only.
If you require more accuracy, then change the 105.3 to something like 105.26 or perhaps 105.263 or whatever you prefer to round to; there are infinitely many ways to write this value because we're dealing with a rounded approximation.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! plan A is 40 dollars a day and .19 per mile.
plang B is 60 dollars a say.
your break even point will be when the cost for plan A is equal to the cost for plan B.
let x = the number of miles.
plan A will cost 40 + .19 * x dollars.
plan B will cost 60 dollars.
the costs will be the same when 60 = 40 + .19 * x
subtract 40 from both sides of the equation to get:
20 = .19 * x
solve for x to get:
x = 20 / .19 = 105.2631579 miles.
the cost will be the same when 105.2631579 miles were traveled.
plan A would cost 40 + .19 * 105.2631579 miles = 40 + 20 = 60 dollrs.
plan B would cost 60 dollars.
plan B would save money if more than 105.2631579 miles were traveled.
plan A would save money if less than 105.2631579 miles were traveled.
for exmple:
plan B will always cost 60 dollars a day regardless of the number of miles traveled.
when traveling for 50 miles, which is less than 105.2631579 miles, plan A costs 40 + .19 * 50 = 49.5 dollars which is less than what plan B costs, therefore plan A saves money.
when traveling for 200 miles, which is more than 105.2631579 miles, plan A costs 40 + .19 * 200 = 78 dollars which is more than what plan B costs, therefore plan B saves money.
let me know if you have any questions.
theo
Answer by greenestamps(13200)  (Show Source):
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