Question

John commutes each day to work either by train or by bus. The bus pass costs $10 plus $2 per trip. The train costs $15 plus $1.50 per trip. What is the most number of trips John can make before the bus costs more than the train?

Answer 1

12 trips. At 12 trips, the bus and the train both cost $34 so at 13 trips, the bus trip costs $36 and the train trip costs $35.50.

Answer 2

10

Explanation:

Let n be the no. of trips

Cost of bus pass = $10

Cost of per trip by bus = $2

Cost of n trips by bus 2n

Total cost by Bus= 10+2 n

Cost of Train pass = $15

Cost of per trip by train = $1.50

Cost of n trips by train = 1.50n

Total cost by train = 15+1.50 n

We are supposed to find the most number of trips John can make before the bus costs more than the train

So,
`10+2 n > 15+1.50n`

`10+2 n > 15+1.50 n`

`2 n-1.50 n > 15- 10`

`0.50 n > 5`

`n > (5)/(0.50)`

`n >10`

Hence the most number of trips John can make before the bus costs more than the train is 10 .