Answer:
Price for the child ticket (y) is 5 dollars.
Step-by-step explanation:
Let the price of adult tickets be x and price of child tickets be y.
Since theater sold 8 adult ticket and 2 child tickets for $122, therefore
Price of 8 adult tickets = 8x
Price of 2 child tickets = 2y
According to question,
8x + 2y = 122 ............(1)
8x = 122 -2y
[tex]x = \frac{122 - 2y}{8}[/tex]
[tex]x = \frac{61 - y}{4}[/tex]
Similarly, Price of 5 adult tickets = 5x
Price of 9 child tickets = 9y
According to question,
5x + 9y = 115
By substituting the value of x
= [tex]5(\frac{61 - y}{4}) + 9y = 115[/tex]
= [tex]305 - 5y + 4 (9y) = 115 \times 4[/tex]
= [tex]- 5y + 36 y = 460 - 305[/tex]
= [tex]31 y = 155[/tex]
= [tex]y = \frac{155}{31} = 5\ dollars[/tex]
Therefore the price for the child ticket is 5 dollars.
