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.
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 the possible value of t, we need to consider the total cost of the movie ticket, including the amusement tax.
Let's assume the value of t is x dollars.
The amusement tax on each ticket is 15% of x, which is 0.15x.
So, the total cost of the movie ticket, including the amusement tax, is x + 0.15x = 1.15x dollars.
We are given that the total cost of the movie is greater than $17.50 and less than $20.
Therefore, we have the inequality:
17.50 < 1.15x < 20
To solve this inequality, we can divide all parts of it by 1.15:
17.50/1.15 < x < 20/1.15
15.22 < x < 17.39
Therefore, the value of t (x) could be any value between 15.22 and 17.39 dollars to make Conor's total cost to see the movie possible.
thats wrong
Apologies for the incorrect response. Let me reevaluate the problem.
We are given that the total cost to see the movie is greater than $17.50 and less than $20, including the 15% amusement tax.
Let's assume the ticket price before the tax is t dollars.
The amusement tax on each ticket is 15% of t, which is 0.15t.
So, the total cost of the movie ticket, including the amusement tax, is t + 0.15t = 1.15t dollars.
We know that the total cost is greater than $17.50 and less than $20, so we can set up the following inequality:
17.50 < 1.15t < 20
To solve this inequality, we can divide all parts by 1.15:
15.217391 < t < 17.391304
Therefore, the value of t (the ticket price before tax) could be any value between approximately $15.22 and $17.39 to make Conor's total cost to see the movie possible.
To find the possible value of t, we need to consider the cost of the ticket with the amusement tax included.
Let's assume the value of t to be x dollars, where x is the cost of the ticket without the tax.
According to the given information, the total cost including the tax must be greater than $17.50 and less than $20.
So, we can set up the following inequality to represent this:
x + 0.15x > $17.50 (to be greater than $17.50)
1.15x > $17.50
Solving for x:
x > $17.50 / 1.15
x > $15.22
Now, let's set up another inequality:
x + 0.15x < $20 (to be less than $20)
1.15x < $20
Solving for x:
x < $20 / 1.15
x < $17.39
So, the possible value of t to make it possible for Conor's total cost to be greater than $17.50 and less than $20 is any value between $15.22 and $17.39.
To find the possible values of t, we can start by calculating the total cost including the amusement tax.
Let's assume the ticket price is t dollars.
Given that there is a 15% amusement tax on each ticket, the tax amount would be 0.15t dollars.
The total cost, including the tax, would be the sum of the ticket price and the tax amount: t + 0.15t = 1.15t dollars.
Based on the information provided, we know that the total cost must be greater than $17.50 and less than $20. Therefore, we can set up the following inequality:
17.50 < 1.15t < 20
To find the possible values of t, we can solve this inequality by dividing all sides by 1.15:
15.22 < t < 17.39
Therefore, the possible values of t that would make the total cost fall within the given range are between $15.22 and $17.39.