Movie theater a has a popcorn machine with 120 gallon capacity. It sells 7 gallons of popcorn per hour movie theater B has a popcorn machine with 150 gallon capacity. It sells 9 gallons of popcorn per hour right and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.

Answer 1

Let's represent the amount of popcorn left in theater A after x hours as P(x) and the amount of popcorn left in theater B after x hours as Q(x).

From the given information, we know that:
P(0) = 120 (initial capacity of theater A)
Q(0) = 150 (initial capacity of theater B)
P(x) = 120 - 7x (popcorn left in theater A after x hours)
Q(x) = 150 - 9x (popcorn left in theater B after x hours)

To find when the two theaters will have the same amount of popcorn left, we need to solve the equation P(x) = Q(x).

120 - 7x = 150 - 9x

To simplify, we combine like terms:
9x - 7x = 150 - 120

2x = 30

Dividing both sides by 2:
x = 15

Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.