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?

To determine a value of \( t \) that would make Conor's total cost to see the movie greater than $17.50 and less than $20, we need to know the relationship between \( t \) and the total cost.

Assuming \( t \) is a fixed price for the ticket, let's denote the total cost for seeing the movie as a function of \( t \):

\[ \text{Total Cost} = \text{Ticket Price (t)} + \text{Other Costs} \]

If we only consider the ticket price and assume there are no other costs, the total cost would simply be \( t \). Therefore, for \( t \) to fall into the specified range:

\[ 17.50 < t < 20 \]

This tells us that \( t \) must be a value strictly greater than $17.50 and strictly less than $20.

Values that would satisfy this condition could include:

• \( t = 18 \)
• \( t = 19.99 \)
• \( t = 19.50 \)

Any value between $17.51 and $19.99 would work.

If there are additional costs involved beyond the ticket price, you'll need to specify those to refine the value of \( t \) further.

If the value of \( t \) is $0.15 and this represents some form of cost (like a transaction fee, tax, or additional charge), we can incorporate that to find Conor's total cost to see the movie.

Here’s how we can approach it:

1. Determine total cost: If the total cost is influenced by \( t = 0.15 \), we can express the total cost as: \[ \text{Total Cost} = \text{Base Cost} + t \]

2. Set the condition: We know the total cost must be greater than $17.50 and less than $20: \[ 17.50 < \text{Total Cost} < 20 \]

3. Substituting \( t \): Using \( t = 0.15 \): \[ 17.50 < \text{Base Cost} + 0.15 < 20 \]

4. Isolating the base cost:

   • For the lower boundary: \[ \text{Base Cost} + 0.15 > 17.50 \] \[ \text{Base Cost} > 17.50 - 0.15 \] \[ \text{Base Cost} > 17.35 \]

   • For the upper boundary: \[ \text{Base Cost} + 0.15 < 20 \] \[ \text{Base Cost} < 20 - 0.15 \] \[ \text{Base Cost} < 19.85 \]

5. Resulting Range: Therefore, the base cost must satisfy: \[ 17.35 < \text{Base Cost} < 19.85 \]

In conclusion, if \( t = 0.15 \), then the base cost of the movie ticket (or additional fees) needs to fall within the range of $17.35 and $19.85 for Conor’s total cost to be more than $17.50 and less than $20.

Sure! Let's break it down simply.

1. Understanding \( t \): If \( t = 0.15 \), this could be a small fee, like a tax or a service charge that Conor pays when buying his movie ticket.

2. Total Cost: We want to know how much Conor's total cost is to see the movie. To find this, we can say:

   \[ \text{Total Cost} = \text{Base Cost} + 0.15 \]

3. Setting the Limits: We know that the total cost needs to be more than $17.50 and less than $20. We can write this out like this:

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

4. Plugging in \( t \): Now, let’s use our value of \( t = 0.15 \):

   \[ 17.50 < \text{Base Cost} + 0.15 < 20 \]

5. Finding the Base Cost: We need to figure out what the base cost (the main price of the ticket) should be:

   • For the lower part: \[ 17.50 < \text{Base Cost} + 0.15 \] To find the base cost, we subtract \( 0.15 \) from \( 17.50 \): \[ \text{Base Cost} > 17.50 - 0.15 = 17.35 \]

   • For the upper part: \[ \text{Base Cost} + 0.15 < 20 \] Again, we subtract \( 0.15 \) from \( 20 \): \[ \text{Base Cost} < 20 - 0.15 = 19.85 \]

6. Final Answer: So the base cost of the ticket must be: \[ 17.35 < \text{Base Cost} < 19.85 \]

This means that for Conor’s total cost to be between $17.50 and $20, the main cost of the movie ticket (before adding the extra $0.15) needs to be more than $17.35 and less than $19.85.

In simpler terms, the main price of the ticket needs to be between $17.36 and $19.84.