Question

The Student council sponsored a talent show to raise money. They charged 5 dollars admission for each adult and 2 dollars for each student . A total of 248 people attend the show and the made 715 dollars. How many students attended the talent show.

Answer 1

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

`\begin{gathered} x+y=248\ldots\text{eqn}(1) \\ 5x+2y=715\ldots eqn(2) \end{gathered}`

Solving the pair of equations simultaneously by elimination method:

To eliminate the terms in x, we multiply through eqn(1) by 5 to get,

`\begin{gathered} 5(x+y=248) \\ 5x+5y=1240\ldots eqn(3) \end{gathered}`

Subtracting eqn(2) from eqn(3), we get

`\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=(525)/(3)=\text{ 175 students} \end{gathered}`

Thus, the number of students that attended the talent show is 175.