Let [tex]x[/tex] be the tickets that the adults bought, and[tex] y[/tex] be the tickets that children bought.
From the problem we have the system of linear equations:
[tex] \left \{ {{2x+5y=2686} \atop {y=3x}} \right. [/tex]
The first thing we are going to do to solve our system, is replacing equation (2) in equation (1), and then, solve for [tex]x[/tex]
[tex]2x+5y=2686[/tex]
[tex]2x+5(3x)=2686[/tex]
[tex]2x+15x=2686[/tex]
[tex]17x=2686[/tex]
[tex]x= \frac{2686}{17} [/tex]
[tex]x=158[/tex]
Now that we have the number of tickets that the adults bought, lets replace that value in equation (2):
[tex]y=3x[/tex]
[tex]y=3(158)[/tex]
[tex]y=474[/tex]
Last but not least, to find the total number of tickets, we are going to add [tex]x[/tex] and [tex]y[/tex]:
[tex]158+474=632[/tex]
We can conclude that Northwest High School's senior class sold 632 raffle tickets.
