Problem:
Number Concepts-Fractions and Decimals
(InterMath)
A car rental agency charges $37.50 per day and $0.23
per mile or fraction thereof to rent a car.
A bus ticked cost$85.75 round trip.
Under what circumstances is each option more economical?
Solution:
x = number of miles driven
Cost formula of rental car company for one day of use:
f(x)= .23x + 37.50
Cost formula for the bus ticket (it is a constant and
does not change):
f(x)= 85.75
The solution to this problem is contextual:
If you plan on having the rental car more than 2 days, than the
bus is more economical. However, if the trip is 2 days or less
the car would appear more economical.
If it is a one day trip, the car is more economical. This is true
only if you travel less than 210 miles. If you go over 210 miles
in 1 day than the bus becomes more economical.
1 day trip:
85.75= .23x + 37.50
48.25 = .23x
209.8 = x
For a two day trip you would have to travel less than
24 miles a day in the rented car. If you went over 24 miles each
day, the bus would be more economical.
2 day trip:
85.75 = 2 (.23x+ 37.50)
85.75 = .46x +75
10.75 = .46x
23.4 = x
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