Question

1. My sister Courtney is an assistant professor at a major university and a licensed psychologist. She was invited to speak at a conference in Philadelphia and brought along her husband and two kids for the conference on the flight to the “city of brotherly love”. After making it to Philly, the family needed a taxi to get to the hotel they were staying. So Courtney used the Reunion Cab Company for their transportation. It costs $3.15 for entry into the cab and $1.75 for each additional passenger. Mr. De Palma, the taxi driver, charges $0.45 for every two-ninths of a mile traveled in his vehicle. Once Courtney and her family made it to the hotel, she used her credit card to pay Mr. De Palma $42.00, which included a tip. The amount paid to Mr. De Palma was exactly eight times the amount Courtney gave for a tip. How many miles did Courtney and her family travel in Mr. De Palma’s cab? (Decimals are okay for this problem, but no rounding should be done at any time.)

Answer 1

Start with all the fixed costs

• Entry into the cab = 3.15
• Cost of three extras = 3*1.75 = 5.25
• Tip = 42/8 = 5.25

Total Fixed Costs 13.65

Amount Spent on Mileage 42 - 13.65=28.35

Now set up the proportion for the mileage using cost

2/9 mile = x

0.45 cents 28.35

Multiply both sides by 28.35

(2/9) * 28.35 / 0.45 = x

Put this into your calculator as

(

2/9

)

*

28.35

/

0.45

=

14

The answer is 14 miles traveled.