A ticket to a movie costs t dollars, and there is a 15% amusement tax on each ticket.
Conor buys a ticket to see a movie. Write two expressions in terms of t showing his total cost.
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.
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?
Two expressions in terms of t showing Conor's total cost are:
1) Total cost including tax: t + (0.15*t)
2) Total cost without tax: t
Let's choose a value for t = $12.50. Using expression 1), the total cost would be:
Total cost = 12.50 + (0.15*12.50)
Total cost = 12.50 + 1.875
Total cost = $14.375
To find a value of t that would make Conor's total cost greater than $17.50 and less than $20, we can set up the following inequality using expression 1):
t + (0.15*t) > 17.50 and t + (0.15*t) < 20
Solving the inequalities, we find:
1.15*t > 17.50 and 1.15*t < 20
t > 15.22 and t < 17.39
So, a possible value of t that would make Conor's total cost fall within that range could be t = $16.