We will represent adults as x and students as y. Each adult ticket was $5 and each student ticket was $3, so we can write the equation as 5x + 3y = 460 We also know that the total number of tickets sold between the students and adults was 120. A second equation we make because of that is x + y = 120 Now we have to ways to represent x and y and we need to use one to solve the other. I am going to rearrange the second equation to get y by itself. y = 120 - x Now we plug this equation in for y in the top equation so 5x + 3y = 460 becomes 5x + 3(120 - x) = 460 then we distribute 5x + 360 - 3x = 460 combine like factors 2x + 360 = 460 2x =100x = 50 So we sold 50 adult tickets (x) and since there were 120 tickets sold total we know that we sold 70 student tickets Then we double check our math. 50 adult tickets x $5 each is $250 70 student tickets x $3 each = $210 $210 + $250 = $460 Answer: 50 adult tickets and 70 student tickets
