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?

Question

11 trips

10 trips

13 trips

15 trips

Answer 1

To compare the costs of the bus and the train for John, we can set up equations based on the given pricing.

1. Bus Cost Calculation:

   • Fixed cost: $10
   • Variable cost per trip: $2
   • Total cost for \( n \) trips: \[ \text{Bus Cost} = 10 + 2n \]

2. Train Cost Calculation:

   • Fixed cost: $15
   • Variable cost per trip: $1.50
   • Total cost for \( n \) trips: \[ \text{Train Cost} = 15 + 1.5n \]

3. Set up the inequality to find when the bus cost exceeds the train cost: \[ 10 + 2n < 15 + 1.5n \]

4. Solve the inequality: \[ 10 + 2n < 15 + 1.5n \] Subtract \( 1.5n \) from both sides: \[ 10 + 0.5n < 15 \] Subtract 10 from both sides: \[ 0.5n < 5 \] Multiply both sides by 2: \[ n < 10 \]

This means that John can make up to 9 trips before the bus becomes more expensive than the train.

Conclusion: The most number of trips John can make before the bus costs more than the train is 9 trips. Since this option is not provided in your choices, it seems there may be a misinterpretation of the question or choices. However, considering the question asked for the maximum number of trips before the cost changes, 9 trips would be the answer.

If we re-evaluate the options available, the threshold where John reaches 10 trips he would be at an equal cost to the train, where at 11 trips the bus would definitely cost more. Hence the answer is effectively \( 10 \) as the highest before the cost exceeds.