Problema Solution
4. Papalia and his friends are going on a road trip and they would like to rent a car. There are three options of rental cars for he and his friends.
Option 1: $180 for three days plus $.41/km.
Option 2: $275 for the three days plus $.21/km
Option 3: $425 for the three days and no additional charge
a) At what distance travelled will each option become the most prudent ?
b) If the total trip from destination to destination approximately 700 km, what option should Papalia choose? Justify what factors he should take into consideration when making this choice.
Answer provided by our tutors
let 'x' be the distance traveled in km in 3 days
Option 1: he will spend 180 + 0.41x
Option 2: he will spend 275 + 0.21x
Option 3: he will spend 425
a)
- Option 1 is the best option when
180 + 0.41x < = 275 + 0.21x
180 + 0.41x < 425
or
x <= 475
x < 597.57
x is element of (0, 475]
he travels not more than 475 km.
- Option 2 is the best option when
275 + 0.21x <= 180 + 0.41x
275 + 0.21x <= 425
or
x>= 475
x <= 714 2/7
x is element of [475, 714 2/7]
he travels not less then 475 km and not more than 714 2/7 km
- Option 3 is the best option when
425 <= 180 + 0.41x
425 <= 275 + 0.21x
or
x => 597 23/41
x => 714 2/7
x is element of [714 2/7, ~)
he travels not less than 714 2/7 km.
b)if the total trip is 700 km
700 is element of [475, 714 2/7] thus he should chose Option 2.