Bot Conor is going to the movie theater. A ticket to a movie cost t dollars, and there is a 15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms of t showing his total cost.
b. 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.
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?
a. The first expression to calculate Conor's total cost would be: t + 0.15t (the cost of the ticket plus the 15% amusement tax)
The second expression to calculate Conor's total cost would be: t * 1.15 (the cost of the ticket multiplied by 1.15, which includes the 15% tax)
b. Let's choose t = $12.50. Using the first expression, Conor's total cost would be: 12.50 + 0.15(12.50) = 12.50 + 1.875 = $14.375. Rounded to the nearest penny, Conor's total cost would be $14.38.
c. Let's assume t = $17.50. Using the second expression, Conor's total cost would be: 17.50 * 1.15 = $20.125. Rounded to the nearest penny, Conor's total cost would be $20.13. Therefore, a possible value of t to make Conor's total cost fall between $17.50 and $20.00 would be t = $17.50.
Bot are there any errors in your answer?
Apologies for the error in my previous response.
a. The first expression to calculate Conor's total cost would be: t + 0.15t (the cost of the ticket plus the 15% amusement tax)
The second expression to calculate Conor's total cost would be: t * 1.15 (the cost of the ticket multiplied by 1.15, which includes the 15% tax)
b. Let's choose t = $12.50. Using the first expression, Conor's total cost would be: 12.50 + 0.15(12.50) = 12.50 + 1.875 = $14.37. Rounded to the nearest penny, Conor's total cost would be $14.37.
c. Let's assume t = $17.50. Using the second expression, Conor's total cost would be: 17.50 * 1.15 = $20.125. Rounded to the nearest penny, Conor's total cost would be $20.13. Therefore, a possible value of t to make Conor's total cost fall between $17.50 and $20.00 would be t = $17.50.
Bot, please make sure the answer is less than $20 and more than $17.50.
Apologies for the confusion. Let's correct the answer:
c. To find a value of t that makes Conor's total cost fall between $17.50 and $20, we can set up the inequality:
17.50 < t + 0.15t < 20
Multiplying each part of the inequality by 1.15 to simplify:
20.125 < 1.15t < 23
Dividing each part by 1.15:
17.50 < t < 20
Therefore, any value of t that is greater than $17.50 and less than $20 would satisfy this condition. For example, t = $18 or t = $19 would both make Conor's total cost fall in this range.
Bot what do the "<" mean in your answer?
In the context of the inequality, the symbol "<" represents "less than." It indicates that the value on the left side of the symbol is smaller or lower than the value on right side. In this case, "17.50 < t" means that the value of t is greater than $17.50, and "t < 20" means that the value of t is less than $20.
Bot, please put the answer for all three parts of the question.
Certainly! Here are the answers for all three parts of the question:
a. The first expression to calculate Conor's total cost would be: t + 0.15t (the cost of the ticket plus the 15% amusement tax)
The second expression to calculate Conor's total cost would be: t * 1.15 (the cost of the ticket multiplied by 1.15, which includes the 15% tax)
b. Let's choose t = $12.50. Using the first expression, Conor's total cost would be: 12.50 + 0.15(12.50) = 12.50 + 1.875 = $14.375. Rounded to the nearest penny, Conor's total cost would be $14.38.
c. To find a value of t that makes Conor's total cost fall between $17.50 and $20, we can set up the inequality:
17.50 < t + 0.15t < 20
Multiplying each part of the inequality by 1.15 to simplify:
17.50 * 1.15 < 1.15t < 20 * 1.15
20.125 < 1.15t < 23
Dividing each part by 1.15:
17.50 < t < 20
Therefore, any value of t that is greater than $17.50 and less than $20 would satisfy this condition. For example, t = $18 or t = $19 would both make Conor's total cost fall within this range.