A movie theater offers two options for membership. The first option costs $15 per ticket but an initial fee of $10. The second option costs $10 per ticket but an initial fee of $45. After how many tickets are both options the same price?
__ tickets
Let's assume the number of tickets needed for both options to be the same price is x.
For the first option, the cost is $15 per ticket with an initial fee of $10. So the total cost for x tickets can be represented as 15x + 10.
For the second option, the cost is $10 per ticket with an initial fee of $45. So the total cost for x tickets can be represented as 10x + 45.
Since we want the total cost for x tickets to be the same for both options, we can set the equations equal to each other:
15x + 10 = 10x + 45
Subtracting 10x and 10 from both sides:
5x = 35
Dividing both sides by 5:
x = 7
Therefore, both options will be the same price after 7 tickets.
To determine the number of tickets at which both options are the same price, we can set up an equation.
Let's denote the number of tickets as 'x'.
For the first option, the cost per ticket is $15, and there is an initial fee of $10. Therefore, the total cost for 'x' tickets would be 15x + 10.
For the second option, the cost per ticket is $10, and there is an initial fee of $45. So, the total cost for 'x' tickets would be 10x + 45.
To find the point of equality, we'll set up the equation:
15x + 10 = 10x + 45
Now, let's solve the equation for 'x'.
15x - 10x = 45 - 10
5x = 35
x = 35 / 5
x = 7
Therefore, for 7 tickets, both options will cost the same.
To find out after how many tickets both options are the same price, we need to set up an equation based on the given information.
Let's assume that x represents the number of tickets.
For the first option, the cost per ticket is $15 and there is an additional initial fee of $10, so the total cost would be 15x + 10.
For the second option, the cost per ticket is $10, but there is a higher initial fee of $45, so the total cost would be 10x + 45.
Setting up the equation:
15x + 10 = 10x + 45
Now, we can solve this equation to find the value of x:
15x - 10x = 45 - 10
5x = 35
x = 7
Therefore, after 7 tickets, both options will be the same price.