Answer:
[tex]\left\{\begin{array}{l}9x+4y=40.50\\ \\3x+5y=38.25\end{array}\right.[/tex]
The price of one bag of popcorn is $1.20
Step-by-step explanation:
Let x be the price of one drink and y be the price of one bag of popcorn.
Chase:
He spends a total of $40.50 on 9 drinks which cost $9x and on 4 bags of popcorn which cost $4y. Hence,
[tex]9x+4y=40.50[/tex]
Oliver:
He spends a total of $38.25 on 3 drinks which cost $3x and on 5 bags of popcorn which cost $5y. Then
[tex]3x+5y=38.25[/tex]
Write a system of two equations:
[tex]\left\{\begin{array}{l}9x+4y=40.50\\ \\3x+5y=38.25\end{array}\right.[/tex]
To solve this system of two equations, multiply the second equation by 3
[tex]\left\{\begin{array}{l}9x+4y=40.50\\ \\9x+15y=114.75\end{array}\right.[/tex]
and subtract the first equation from the secoond:
[tex](9x+15y)-(9x+5y)=114.75-40.50\\ \\9x+15y-9x-5y=74.25\\ \\10y=74.25\\ \\y=7.425[/tex]
Substitute [tex]y=7.425[/tex] into the first equation:
[tex]9x+4\cdot 7.425=40.50\\ \\9x+29.7=40.50\\ \\9x=40.50-29.7\\ \\9x=10.8\\ \\x=1.2[/tex]
The price of one bag of popcorn is $1.20
