Question

(10 points): 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.)
please show all work

Answer 1

Courtney and her family traveled 14 miles in Mr. De Palma's cab from the airport to the hotel.

Explanation:

The total amount of the ride, including tip, was $42.00. Since this amount represents exactly eight times the amount that was received as a tip, 42/8 is $5.25, which is the cost of the tip. The other flat rates associated with the trip is the $3.15 for entry and $1.75 for each additional passenger (1.75 x 3=5.25). Once you subtract these fees from the total amount, $42 - $5.25 (tip) - $5.25 (additional passengers) - $3.15 (entry) = $28.35. Since Mr. De Palma charges $0.45 for every two-ninths of a mile, you take the revised total 28.35/.45 = 63. Since 63 represents the amount for every two-ninths of a mile, you need to multiply this amount by 2/9 to get your total amount of miles, or 63 x 2/9 = 14.