A movie theater offers two options for memberships. The first option costs 10$ per ticket but an initial fee of 20$ the second option 5$ per ticket but a initial fee of 50$ after how many tickets are both options the same price

1 answer

Let's represent the total cost of the first option as 10x + 20, where x is the number of tickets purchased. The total cost of the second option can be represented as 5y + 50, where y is the number of tickets purchased.

To find out when both options are the same price, we need to set the two equations equal to each other:

10x + 20 = 5y + 50

Subtract 20 from both sides:

10x = 5y + 30

Divide by 5:

2x = y + 6

Now we can substitute y for 2x in the second option equation and solve for x:

5(2x) + 50 = 10x + 20
10x + 50 = 10x + 20
50 = 20

This equation has no solution, meaning that the two options will never be the same price.