A ticket to a movie costs t dollars, and there is a 15% amusement tax on each ticket.
1.Conor buys a ticket to see a movie. Write two expressions in terms of t showing his total cost.
2.Choose a value for t greater than $12 and less than $13. Use one of the expressions you wrote in part a) to find Conor’s total cost, rounded to the nearest penny. Show your work.
3.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. The two expressions showing Conor's total cost are:
- t + 0.15t (this represents the ticket cost plus the 15% amusement tax)
- 1.15t (this represents the total cost after adding the 15% amusement tax)
2. Let's choose t = $12.50 as a value within the given range. Using the expression 1.15t:
Total cost = 1.15 * $12.50 = $14.38 (rounded to the nearest penny)
3. Let's assume t = $16. Using the expression 1.15t:
Total cost = 1.15 * $16 = $18.40 (which is within the given range)
Please show how you got that understandingly
Apologies for the confusion. Let's go through each part step by step.
1. Conor buys a ticket to see a movie. The ticket cost is t dollars. Since there is a 15% amusement tax on each ticket, we need to calculate the total cost.
Expression 1: t + 0.15t
Here, t represents the ticket cost, and 0.15t represents 15% of the ticket cost, which is the amusement tax. Adding these two together gives us the total cost of the ticket with the amusement tax included.
Expression 2: 1.15t
In this expression, we combine the ticket cost with the amusement tax directly. 1.15 represents 100% (the ticket cost) plus 15% (the amusement tax), so when we multiply it by t, we get the total cost.
2. To find Conor's total cost with a value of t between $12 and $13, we can use one of the expressions from part 1. Let's use expression 2: 1.15t.
Let's choose t = $12.50.
Total cost = 1.15 * $12.50
= $14.375
Rounded to the nearest penny, the total cost is $14.38.
So, Conor's total cost (rounded to the nearest penny) with a ticket cost of $12.50 would be $14.38.
3. Suppose Conor's total cost to see the movie is between $17.50 and $20. We need to find a value of t that makes this possible.
Let's assume t = $16.
Total cost = 1.15 * $16
= $18.40
Since $18.40 is within the given range ($17.50 and $20), a value of t = $16 would make it possible for Conor's total cost to be within that range.
1. To calculate Conor's total cost, we need to consider the cost of the ticket and the amusement tax. Let's write two expressions in terms of t:
Expression 1: t + (0.15t)
This expression represents the cost of the ticket (t) plus the amusement tax (0.15t).
Expression 2: 1.15t
This expression combines the ticket cost and the amusement tax into a single term. We multiply the ticket cost (t) by 1.15 to include the 15% amusement tax.
2. Let's choose a value for t between $12 and $13 and use Expression 1 to calculate Conor's total cost rounded to the nearest penny. For example, let's choose t = $12.50:
Total Cost = t + (0.15t)
= $12.50 + (0.15 * $12.50)
= $12.50 + $1.875
≈ $14.375 (rounded to the nearest penny)
= $14.38
Therefore, Conor's total cost, when t = $12.50, would be approximately $14.38.
3. If Conor's total cost to see the movie is greater than $17.50 and less than $20, we need to find a value of t that satisfies this condition. Let's assume a value of t and check if it falls within the given range.
Let's start with t = $18:
Total Cost = 1.15t
= 1.15 * $18
= $20.70
The total cost exceeds $20. Thus, t = $18 does not satisfy the condition.
Now, let's try t = $19:
Total Cost = 1.15t
= 1.15 * $19
≈ $21.85
The total cost is higher than $20, so t = $19 does not satisfy the condition either.
Finally, let's try t = $17.75:
Total Cost = 1.15t
= 1.15 * $17.75
≈ $20.31
The total cost falls within the given range ($17.50-$20) as it is approximately $20.31. Therefore, a possible value of t to make Conor's total cost fall between $17.50 and $20 is approximately $17.75.