Let x be the number of couple tickets and let y be the number of single tickets sold.
We know that the school earned a total of $7050, then we have that:
[tex]75x+50y=7050[/tex]Now, we also know that the total number of students was 173, then we have:
[tex]2x+y=173[/tex]Hence we have the system of equations:
[tex]\begin{gathered} 75x+50y=7050 \\ 2x+y=173 \end{gathered}[/tex]To solve this system we multiply the second equation by -50, then we have:
[tex]\begin{gathered} 75x+50y=7050 \\ -100x-50y=-8650 \end{gathered}[/tex]Adding this equation we have:
[tex]\begin{gathered} -25x=-1600 \\ x=\frac{-1600}{-25} \\ x=64 \end{gathered}[/tex]Once we know the value of x we plug it in the second equation to get y:
[tex]\begin{gathered} 2(64)+y=173 \\ y=173-128 \\ y=45 \end{gathered}[/tex]Therefore, they sold 64 couple tickets and 45 single tickets.
