Let 'x' represent the number of child tickets.
Let 'y' represent the number of adult tickets.
Given
The total number of tickets are 139,
[tex]x+y=139\ldots\ldots\ldots1[/tex]
The total sales of tickets sold were $1016.20.
[tex]6.10x+9.40y=1016.20\ldots\ldots\ldots.2[/tex]
Let us combine the two equations together and resolve for y using the Substitution method of simultaneous equation
[tex]\begin{gathered} x+y=139\ldots\ldots\ldots1 \\ 6.10x+9.40y=1016.20\ldots\ldots\ldots.2 \end{gathered}[/tex]
Make x the subject of formula from equation 1,
[tex]\begin{gathered} x+y=139 \\ \therefore x=139-y \end{gathered}[/tex]
Substitute x = 139 - y into equation 2 and solve for y
[tex]6.1\mleft(139-y\mright)+9.4y=1016.2[/tex]
Simplify
[tex]\begin{gathered} 847.9-6.1y+9.4y=1016.2 \\ 847.9+3.3y=1016.2 \\ 3.3y=1016.2-847.9 \\ 3.3y=168.3 \\ \text{Divide both sides by 3.3} \\ \frac{3.3y}{3.3}=\frac{168.3}{3.3} \\ \therefore y=51 \end{gathered}[/tex]
Hence, the number of adult tickets sold were 51 tickets.
