Conor is going to the movie theater. 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.
The first expression to show Conor's total cost would be t + 0.15*t, which accounts for the cost of the ticket plus the 15% amusement tax.
The second expression to show Conor's total cost would be (1 + 0.15)*t, which simplifies to 1.15*t. This expression can also be used to calculate Conor's 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.
Let's choose t = $12.50 as a value that is greater than $12 and less than $13.
Using the expression t + 0.15*t, we can calculate Conor's total cost:
Total cost = 12.50 + 0.15*12.50
= 12.50 + 1.875
= 14.375
Rounded to the nearest penny, Conor's total cost is $14.38.
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 find a value of t that would make Conor's total cost to see the movie greater than $17.50 and less than $20, we can use the second expression: (1 + 0.15)*t = 1.15*t.
Let's start by assuming the total cost is $17.50:
17.50 < 1.15*t
Dividing both sides by 1.15, we get:
t > 17.50/1.15
t > 15.22
Next, let's assume the total cost is $20:
1.15*t < 20
Dividing both sides by 1.15, we get:
t < 20/1.15
t < 17.39
Therefore, a value of t that would make Conor's total cost greater than $17.50 and less than $20 would be any value of t between 15.22 and 17.39.