If x represents adult tickets and y represents child tickets, we have 8x+5y=177.50 . There are infinite solutions due to that you can plug in any number for x and still find a number for y that fits, so I'll solve for a child ticket in terms of an adult ticket and vice versa. For an adult ticket, we subtract 5y from both sides and then divide by 8, getting (177.5-5y)/8. For a child ticket, we subtract 8x from both sides and divide by 5, getting (177.50-8x)/5