Transit Transaction - Part II

Algebra Level 1

Calvin lives in San Francisco and commutes to work. In the month of March 2014, he will be taking a direct bus to and from work on Mondays, Wednesdays and Fridays, and he will be driving to Oakland on Tuesdays and Thursdays. He can choose from several options of payment:

Pay $2 for each (one-way) trip.
Pay $15 for a day pass
Pay $29 for a week pass
Pay $66 for a monthly pass

If Calvin doesn't use the bus otherwise, which option will be the cheapest for him?

Buy a weekly pass Buy a monthly pass Pay for each trip individually A combination of different methods

8 solutions

Prasun Biswas
Feb 5, 2014

If we take his cost for 1 month for travelling, we get ----

i) If he pays for each trip, then he has to pay a total of $\$(2+2)=\$4$ each day, first $\$2$ for going and second $\$2$ for returning. Then for 3 days in each week, he pays $=\$(4\times 3)=\$12$ each week and for 4 weeks(a month), he pays $=\$(12\times 4)=\$48$ to go to work for a month.

ii) If he takes a day pass, he has to pay $\$15$ for every work day but we saw that if he pays each trip separately, it costs lower than this, so day pass can be ruled out.

iii) If he takes week pass, he has to pay $\$29$ for every week but we saw that if he pays each trip separately, it costs lower than this, so week pass can be ruled out.

iv) If he takes monthly pass, he has to pay $\$66$ for each month but we saw thatif he pays each trip separately, it costs lower than this, so monthly pass can be ruled out.

v) Even we can see that no combination of different modes of transport can cost less than $\$48$ in a month.

Thus, the answer is Pay for each trip individually.

Aritri Chatterjee
Feb 4, 2014

simple, he works on alternate days, so that makes 12$ and 4 weeks a month so 48$ < 66$ , so a daily pay of 2$ per trip is cheaper...

well if we either don't know which day is occurring more than 4 times (out of M W F) better we use "best probabilistic outcome approach". see if the month is starting with any of the day (M or W) then there will be probability that 3 extra days of the month will have at least 2 extra (M,W) or (W,F)

(in march there are 31 days 28+3 (extra days) )

(Favorable or say Worst condition ) :p so collectively there are (3 4=) 12 days + 2extra favorable days = 14 days on which he would pay for the transit. now $4 a day makes it 14 4=$56 < $66

so $2 per trip is the cheapest way even in the worst case too :)

Sachin Mourya - 7 years, 4 months ago

yes rit

Abhishek Kumar - 7 years, 4 months ago

I am not clear . How will he drive to Oakland on Tuesdays and Thursdays?

Muhammad Zahid - 7 years, 3 months ago

Assume he has a car

Vignesh Raman - 7 years, 3 months ago

Mohammad Ahmed - 7 years, 4 months ago

It's quite easy. In March 2014 there are 5 Mondays and 4 times of Wednesdays and Fridays. If we calculate the fee for one-way trips, it will be 13 x 2 x $2.00, which is $52 a month. It's cheaper than the weekly pass for a month ($116) and the monthly pass ($66).. so it's better to pay for each trips.

Wilson Liu - 7 years, 4 months ago

Saba Majeed
Feb 4, 2014

as for man 13 working days in month march then 13x4=52 if pay for each trip 13x15=195 if pay for a day 4x29=116 if pay for a week 1x66=66 if pay monthly so cheapest is pay for each trip.

Muhamed Medo
Mar 6, 2014

paying fo each trip individualy is cheaper for him because in this option he had to pay 4$ a day and as he went 3 times aweek he would pay 12$ so he pay 48$ each month. but if he use the option of 15$ aday he would pay 45$ each week and 180$ in each month. also if he use the option of 29$ a week he would pay 116$ in one month . and the last option of 66$ monthly was also more than the first one so the answer is 2$ for one-way trip

Krishna Garg
Feb 20, 2014

He travels Total 21 days to work in March 2014.,and by bus 12 days in month and thus pays 12x4== 48 $ other days he travels by car. so other ways to commutte are costlier.Therefore he must travel paying daily 4 $ by bus.

Brandon Lam
Feb 16, 2014

In March 2014, there are 13 Mondays,Wednesdays,and Fridays. For the one day trip, it would be 2 dollars for 2 trips for 13 days, or 52 dollars. For the day pass, it would be 15 dollars for 13 days, or 195 dollars. For the week pass, it would be 29 dollars for 4 weeks + 1 monday, or 145 dollars. For the monthly pass, it would obviously be 66 dollars. The cheapest option would be to purchase individual tickets.

Tootie Frootie
Feb 13, 2014

only 2 rs. for per trip .. as he has to travel by bus on only Mondays, Wednesdays and Fridays so no need of buying weeks or month passes

Ameya Kale
Feb 7, 2014

It can be simply calculated by taking the cost for each day and finding the cost for 4 weeks (28 days) .

Now March has 31 days, so for the remaining 3 days we calculate the cost, seeing that there'll be not more than 2 working days. Hence the cost for the month by daily expense = 52 or 56$

We can easily see that the day pass would be inefficient and expensive : for 31 days, cost of the day pass = 465$!

Cost of week pass = 29$ . Now for 3 weeks (no need to take 4 here), the cost becomes = 87$ .

And monthly pass is for 66$.

Hence the most cost-effective way is to pay per trip.

Since March has 31 days, so we have 4 weeks & 3 days say nay 3 cont. days Mon, Tue, Wed out of which he has to work for 2 days.So total no. of working days becomes 14. Now for each separate trip calculating 2$, we get 56$. While for rest of the option we get more than that so they are ruled out. Even if we take the last 3 days as Sat, Su, Mon still we get the same ans as option 1.

Niraj Mishra - 7 years, 4 months ago

Transit Transaction - Part II

8 solutions

0 pending reports