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