For this case we propose a system of equations:
x: Represents the amount of small popcorn tubs
y: Represents the amount of large popcorn tubs
According to the data we have to:
[tex]3x + 4y = 24[/tex] (Spending all the money in your wallet)
[tex]x + y = 7[/tex] (Buying 7 popcorn tubs)
From the second equation we have:
[tex]x = 7-y[/tex]
Substituting in the first equation:
[tex]3 (7-y) + 4y = 24\\21-3y + 4y = 24\\21 + y = 24\\y = 24-21\\y = 3[/tex]
Thus, Katie can buy 3 large tubs of popcorn.
So:
[tex]x = 7-3\\x = 4[/tex]
In addition, you can buy 4 small tubs of popcorn.
Answer:
3 large popcorn tubs.
4 small popcorn tubs.
