The Solution.
Let the number of adults that attended the show be x ;
and the number of students that attended the show be y.
Representing the problem in equations, we get
[tex]\begin{gathered} x+y=248\ldots\text{eqn}(1) \\ 5x+2y=715\ldots eqn(2) \end{gathered}[/tex]Solving the pair of equations simultaneously by elimination method:
To eliminate the terms in x, we multiply through eqn(1) by 5 to get,
[tex]\begin{gathered} 5(x+y=248) \\ 5x+5y=1240\ldots eqn(3) \end{gathered}[/tex]Subtracting eqn(2) from eqn(3), we get
[tex]\begin{gathered} 5x+5y=1240\text{ ...eqn(3)} \\ -(5x+2y=715)\ldots eqn(2) \\ So, \\ 3y=525 \\ \text{Dividing both sides by 3, we get} \\ y=\frac{525}{3}=\text{ 175 students} \end{gathered}[/tex]Thus, the number of students that attended the talent show is 175.
