Katie wants to buy some popcorn for her family at the theater. Each small tub of popcorn costs $3 and each large tub of popcorn costs $4. She needs to buy at least 7 tubs of popcorn, but she only has $24 in her wallet.

For this case we propose a system of equations:x: Represents the amount of small popcorn tubsy: Represents the amount of large popcorn tubsAccording 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.