Simultaneous Equations In Practical Use

A theatre charges $25 for adults and $15 for children. All 200 seats in the theatre were sold on opening night and the ticket sales totalled $4350. Calculate the number of adult tickets sold.

$\begin{array}{lrcll} x = \text{adults}\\ y = \text{children}\\ \\ \hline (1) & x + y &=& 200 \qquad & |\qquad -x \\ & y &=& 200 - x \\ \hline (2) & x\cdot 25 + y \cdot 15 &=& 4350 \qquad & |\qquad : 3 \\ & x\cdot 5 + y \cdot 3 &=& 870 \qquad & |\qquad y = 200 - x\\ & x\cdot 5 + ( 200 - x) \cdot 3 &=& 870 \\ & x\cdot 5 + 200 \cdot 3 - x \cdot 3 &=& 870 \\ & 5x + 200 \cdot 3 - 3x &=& 870 \\ & 5x + 600 - 3x &=& 870 \qquad & |\qquad -600 \\ & 5x - 3x &=& 870 -600 \\ & 2x &=& 270 \qquad & |\qquad : 2 \\ & \mathbf{ x } & \mathbf{=}& \mathbf{135}\\ \hline & y &=& 200 -x \qquad & |\qquad x = 135 \\ & y &=& 200-135 \\ & \mathbf{ y } &\mathbf{=}& \mathbf{65}\\ \hline \end{array}$

The number of adult tickets sold is 135.

Maybe a little easier this way:  x = adults    200 - x = children

25x  = money from adult tix      15(200 - x) = money from child tix

25x + 15(200-x) = $ 4350

25x+ 3000 - 15x = 4350

10x = 1350      x = 135   = adults      children = 200 - 135 = 65