Question
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.
Answers
Answered by
GPT 3.5
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.
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.