Move theatre A has popcorn machine with 120 gallon capacity. It sells 7 gallons of popcorn per hour. Movie theater B has a popcorn machine with 159 gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left
Let's assume that the amount of popcorn left after "x" hours in theater A is "y" gallons, and the amount of popcorn left after "x" hours in theater B is "z" gallons.
We can write the following equation for both theaters:
120 - 7x = 159 - 9x
To solve this equation, we can simplify it by combining like terms:
7x - 9x = 159 - 120
-2x = 39
Now, divide both sides of the equation by -2 to solve for x:
x = 39 / -2
x = -19.5
Since time cannot be negative, we can conclude that the two popcorn machines will have the same amount of popcorn left after approximately 19.5 hours.
Let's assume "t" hours have passed since the popcorn machines started selling popcorn.
The amount of popcorn remaining in theater A can be calculated using the equation:
Remaining popcorn in theater A = 120 - 7t
The amount of popcorn remaining in theater B can be calculated using the equation:
Remaining popcorn in theater B = 159 - 9t
To find the point at which the two theaters have the same amount of popcorn remaining, we can set the two equations equal to each other:
120 - 7t = 159 - 9t
To solve for "t", we can start by rearranging the equation:
-7t + 9t = 159 - 120
2t = 39
Finally, we can solve for "t" by dividing both sides of the equation by 2:
2t/2 = 39/2
t = 19.5
Therefore, it would take approximately 19.5 hours for both theaters to have the same amount of popcorn left.