Question

26. The school is selling tickets to a music showcase. On the first day of ticket sales the school sold 3 student tickets and 1 adult ticket for a total of $38. The school took in $52 on the second day by selling 3 student tickets and 2 adult tickets. Find the price of a student ticket and the price of an adult ticket.

Answer 1

Let the price of student ticket be x and price of adult ticket be y.

The equation for total cost of ticket on first day is,

$\begin{gathered} 3x+y=38 \\ y=38-3x \end{gathered}$

The equation for total cost of ticket on second day is,

$3x+2y=52$

Substitute 38 - 3x for y in equation to obtain the value of x.

$\begin{gathered} 3x+2(38-3x)=52 \\ 3x-6x=52-76 \\ x=-\frac{24}{-3} \\ =8 \end{gathered}$

Substitute 8 for x in equation y = 38 -3x to obtain the value of y.

$\begin{gathered} y=38-3\cdot8 \\ =38-24 \\ =14 \end{gathered}$

So cost of a student ticket is $8 and cost of a adult ticket is $14.