Given that the children's tickets cost $9 each and the adult tickets cost $19 each. The total number of tickets purchased is 72, and the total amount spent on all the tickets is $808
To Determine: The number of tickets purchased for the children and adult tickets
Solution:
Let the number of tickets purchased for the children be x and the number of tickets purchased for the adult be y
Given that the total number of tickets purchased is 72. Then
[tex]x+y=72====\text{equation 1}[/tex]If the children's tickets cost $9 each. Then the total amount spent to purchase children's tickets would be
[tex]A_{\text{children's tickets}}=x\times9=9x[/tex]If the adult's tickets cost $9 each. Then the total amount spent to purchase adult's tickets would be
[tex]A_{\text{adult's tickets}}=y\times19=19y[/tex]The total amount of money spent to get children and adult tickets is $808. Then,
[tex]9x+19y=808====\text{equation 2}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} x+y=72====\text{equation 1} \\ 9x+19y=808====\text{equation 2} \\ \text{From equation 1,} \\ x=72-y \end{gathered}[/tex]Substitute x in equation 2
[tex]\begin{gathered} 9(72-y)+19y=808 \\ 648-9y+19y=808 \\ -9y+19y=808-648 \\ 10y=160 \\ \text{divide through by 10} \\ \frac{10y}{10}=\frac{160}{10} \\ y=16 \end{gathered}[/tex]Substitute for y in x
[tex]\begin{gathered} x=72-y \\ x=72-16 \\ x=56 \end{gathered}[/tex]The total amount spent to purchase children's and adult tickets would be
[tex]\begin{gathered} 9x=9\times56=504 \\ 19y=19\times16=304 \end{gathered}[/tex]Hence:
Anna purchased 16 adults tickets,
Anna purchased 56 children's tickets
The cost of children's tickets is $504
The cost of adult tickets is $304
