Question

at the city museum, child admission is $6.10 and adult is $9.40. on Tuesday, 139 tickets were sold for a total sales of $1016.20. how many adult tickets were sold that day

Answer 1

Let 'x' represent the number of child tickets.

Let 'y' represent the number of adult tickets.

Given

The total number of tickets are 139,

`x+y=139\ldots\ldots\ldots1`

The total sales of tickets sold were $1016.20.

`6.10x+9.40y=1016.20\ldots\ldots\ldots.2`

Let us combine the two equations together and resolve for y using the Substitution method of simultaneous equation

`\begin{gathered} x+y=139\ldots\ldots\ldots1 \\ 6.10x+9.40y=1016.20\ldots\ldots\ldots.2 \end{gathered}`

Make x the subject of formula from equation 1,

`\begin{gathered} x+y=139 \\ \therefore x=139-y \end{gathered}`

Substitute x = 139 - y into equation 2 and solve for y

`6.1\mleft(139-y\mright)+9.4y=1016.2`

Simplify

`\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} \\ (3.3y)/(3.3)=(168.3)/(3.3) \\ \therefore y=51 \end{gathered}`

Hence, the number of adult tickets sold were 51 tickets.