Question

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?

Answer 1

the value of t is 0.15

Answer 2

this answer needs to be what a 7th grader should know

Answer 3

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.

Answer 4

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.

Answer 5

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.