Answer:
The price of one drink is $10.75
Step-by-step explanation:
Let
$x = price of one drink
$y = price of popcorn.
Autumn:
Autumn spends a total of $156.50 on 2 drinks and 15 bags of popcorn.
Cost of 2 drinks = $2x
Cost of 15 popcorn = $15y
Total cost = $(2x+15y) = $156.50
Kayla:
Kayla spends a total of $59.25 on 3 drinks and 3 bags of popcorn.
Cost of 2 drinks = $3x
Cost of 15 popcorn = $3y
Total cost = $(3x+3y) = $59.25
You get the system of two equations:
[tex]\left\{\begin{array}{l}2x+15y=156.50\\ \\3x+3x=59.25\end{array}\right.[/tex]
Divide the second equation by 3 and express y:
[tex]x+y=19.75\\ \\y=19.75-x[/tex]
Substitute into the first equation:
[tex]2x+15(19.75-x)=156.50\\ \\2x+296.25-15x=156.50\\ \\2x-15x=156.50-296.25\\ \\-13x=-139.75\\ \\13x=139.75\\ \\x=10.75\\ \\y=19.75-10.75=9[/tex]
The price of one drink is $10.75
