Question

jacobs school is selling tickets to a fall musical. On the first day of ticket sales the school sold 2 senior citizens tickets and 6 child tickets for a total of $26. The school took in $54 on the second day by selling 12 senior citizen tickets and 2 child tickets. Find the price of senior citizen ticket and the price of a child ticket.

Answer 1

Let s and c represent the prices of the senior citizen and the child tickets respectively

Then the problem can be modelled as follows:

`\begin{gathered} 2s+6c=26--------------------(1) \\ 12s+2c=54--------------------(2) \\ We\text{ will now solve the simultaneous equation by elimination method} \\ \text{equation (1) }*6\colon \\ 12s+36c=156---------------------(3) \\ 12s+2c=54-----------------------(2) \\ ---------------------------------------- \\ \text{equation (3) - equation (2):} \\ 34c=102 \\ \Rightarrow c=(102)/(34)=3 \\ \text{Substituting the value of c into equation (1), we have:} \\ 2s+6(3)=26 \\ 2s+18=26 \\ \Rightarrow2s=26-18=8 \\ \Rightarrow s=(8)/(2)=4 \end{gathered}`