Question

The school that Natalie goes to is selling tickets to a play. On the first day of ticket sales the school sold 15 adult tickets and 5 student tickets for a total of $265. The school took in $419 on the second day by selling 15 adult tickets and 16 student tickets. What is the price each of one adult ticket and one student ticket

Answer 1

Let x be the price of one adult ticket, and y be the price of one student ticket.

From the information given in the problem, we can set up the following system of equations:

15x + 5y = 265 (equation 1)

15x + 16y = 419 (equation 2)

We can solve for x by subtracting equation 1 from equation 2:

15x + 16y - (15x + 5y) = 419 - 265

11y = 154

y = 14

Now we can substitute y = 14 into either equation 1 or equation 2 to solve for x. Let's use equation 1:

15x + 5(14) = 265

15x + 70 = 265

15x = 195

x = 13

Therefore, one adult ticket costs $13, and one student ticket costs $14.