c. Suppose that Conor’s total cost to see the movie is greater than $17.50 and less than $20. What could be a value of t to make that possible?

1 answer

To determine a value of \( t \) that ensures Conor's total cost to see the movie is greater than $17.50 and less than $20, we need to know how the total cost is calculated in relation to \( t \).

Assuming \( t \) represents the ticket price or some form of additional cost, you would typically set up the inequality for total cost (which we can denote as \( C(t) \)) as follows:

\[ 17.50 < C(t) < 20 \]

Depending on the formula for \( C(t) \), you'll want to find a specific value of \( t \) that satisfies this inequality.

Without specific details about how the cost is structured (e.g., is it a linear function of \( t \)? Does it include other costs such as concessions, taxes, etc.?), let's say if the cost structure is purely \( C(t) = t + f \), where \( f \) might be fixed costs, you could adjust \( t \) accordingly.

For example, if:

  • The cost is calculated simply as \( C(t) = t \) (just the ticket price),
  • Then we want \( t \) values that would fall within this range.

If we take \( t = 18.50 \) as a potential ticket price:

  • \( C(18.50) = 18.50 \), which satisfies \( 17.50 < 18.50 < 20 \).

Thus, \( t = 18.50 \) is a valid answer if the total cost consists solely of the ticket price, which falls within the required range.

If there are additional costs involved, you should adjust \( t \) while factoring in those costs, aiming for a combination that keeps the total cost between $17.50 and $20.