Question

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.

Answer 1

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:

$3x + 4y = 24$ (Spending all the money in your wallet)

$x + y = 7$ (Buying 7 popcorn tubs)

From the second equation we have:

$x = 7-y$

Substituting in the first equation:

$3 (7-y) + 4y = 24\\21-3y + 4y = 24\\21 + y = 24\\y = 24-21\\y = 3$

Thus, Katie can buy 3 large tubs of popcorn.

So:

$x = 7-3\\x = 4$

In addition, you can buy 4 small tubs of popcorn.

Answer:

3 large popcorn tubs.

4 small popcorn tubs.