we can write two equations for the statement, and the solve the system
$2.50 for students and $3 for general admission. If 174 people attended the last gam
![s+g=174](https://img.qammunity.org/2023/formulas/mathematics/college/ws9y1rnblspgu3ehjdwwt4pd87nwk2nzmj.png)
and the box collected $474
![2.50s+3g=474](https://img.qammunity.org/2023/formulas/mathematics/college/k0feopetz7u0z3nbpk2ha5e33pflh2afr9.png)
where s is the number of students and g the number of general admission
![\begin{gathered} s+g=174 \\ 2.50s+3g=474 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ojgybh5h40y8ob33p5fsizbu311czeq48f.png)
to solve the system
we solve a unknow and replace on the other equation ,for example I will solve s from the first equation
![\begin{gathered} s+g=174 \\ s=174-g \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/l621i4mbwms0o3ekj76te9cle7jsjd6jse.png)
now I will replace the value of s on second equation
![\begin{gathered} 2.50s+3g=474 \\ 2.50(174-g)+3g=474 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/nj0mndvq2fljbn19cg4maf7fsdnz9joxk6.png)
simplify
![\begin{gathered} 2.50*174-2.50g+3g=474 \\ 435+0.50g=474 \\ \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/bek3jeho3q9e0ygpwj39ikego4w9y1lxap.png)
and solve for s
![\begin{gathered} 0.50g=474-435 \\ 0.50g=39 \\ g=(39)/(0.50) \\ \\ g=78 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/uqz7x7obnzqfae7e2g1mxpm05qa32unk6g.png)
the value of g (number of general admission) is 78, From this one we can replace the value of g on any equation to solve s
I will replace on the furst equation solved to s
![\begin{gathered} s=174-g \\ s=174-78 \\ s=96 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/u46n97ovwt19zdmau8tclbnbfhgxlv81bt.png)
then the value of s (number of students ) is 96
The box officed sold 78 general admission ticjets and 96 students tickets