Final answer:
The proportional relationship between the number of train tickets (t) and total cost (c) is represented by the equations c = 14t and t = c / 14, which derive from the fact that 3 tickets cost $42, and thus, one ticket costs $14.
Step-by-step explanation:
The total cost of 3 train tickets is $42. We can write two equations to represent the proportional relationship between the number of tickets (t) and the cost (c). Assuming each ticket has the same price, the first equation can be written as c = pt, where p is the price per ticket. Given that 3 tickets cost $42, we find p by dividing $42 by the number of tickets: p = $42 / 3, which gives us p = $14 per ticket. Now we can write the two equations as follows:
- c = 14t (This equation directly states that the cost is 14 times the number of tickets.)
- t = c / 14 (This equation expresses the number of tickets as the cost divided by 14.)
These equations help us understand the budget constraint and tradeoff between purchasing more tickets and the total cost.