Question

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?

Answer 1

To solve the problem, we need to identify a possible value for \( t \) that would result in Conor's total cost being greater than $17.50 and less than $20.

We don't have the exact details for how \( t \) affects the total cost, but we can reason through the implications. Let's assume that \( t \) represents a certain number of items or units of something related to the movie—like tickets, concessions, etc.—and that the cost can be expressed as a function of \( t \).

For example, if the cost function is linear and is represented by:

\[
\text{Total Cost} = \text{Base Cost} + t \times \text{Cost per unit}
\]

To ensure that:

\[
17.50 < \text{Total Cost} < 20
\]

Let's make a simple assumption: if the base cost (like a ticket price) is $15, and the cost per item \( c \) is a certain amount, the equation could look something like this:

\[
\text{Total Cost} = 15 + t \times c
\]

To satisfy the conditions, we can set:

1. **Minimum Condition**:
\[
15 + t \times c > 17.50 \implies t \times c > 2.50 \implies t > \frac{2.50}{c}
\]

2. **Maximum Condition**:
\[
15 + t \times c < 20 \implies t \times c < 5 \implies t < \frac{5}{c}
\]

This gives us a range for \( t \) based on the value of \( c \) (the cost per unit). Let's assume a reasonable \( c \). For instance, if \( c = 1 \) (for simplicity, as if each additional item costs $1), then:

1. \( t > 2.50 \)
2. \( t < 5 \)

Thus, \( t \) can take any integer value between 3 and 4. Alternatively, if \( c \) changes, you can calculate accordingly.

In conclusion, if we assume \( c = 1 \), possible values of \( t \) could be 3 or 4, which will keep the total cost between $17.50 and $20.