Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-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.(1 point)
Responses
120x−7=150x−9 ; x=15
120 x minus 7 equals 150 x minus 9 ; x equals 15
120+7x=150+9x ; x=−15
120 plus 7 x equals 150 plus 9 x ; x equals negative 15
120−7x=150−9x ; x=10
120 minus 7 x equals 150 minus 9 x ; x equals 10
Help
The correct equation is:
120x - 7 = 150x - 9
To solve for x, we can start by subtracting 120x from both sides:
-7 = 30x - 9
Next, we can add 9 to both sides:
2 = 30x
Finally, we can divide both sides by 30 to solve for x:
x = 2/30
Simplified, x = 1/15
So, Movie Theatre A and Movie Theatre B will have the same amount of popcorn left after 1/15 of an hour or 4 minutes.
To find the time when the two popcorn machines will have the same amount of popcorn left, we need to set up an equation.
Let's assume x to be the number of hours passed.
For Movie Theatre A: The amount of popcorn left is 120 - 7x (since it sells 7 gallons per hour and starts with 120 gallons).
For Movie Theatre B: The amount of popcorn left is 150 - 9x (since it sells 9 gallons per hour and starts with 150 gallons).
We want to find the x when the amount of popcorn left is the same for both theaters.
So, the equation becomes:
120 - 7x = 150 - 9x
To solve this equation, we'll combine like terms:
120 + 2x = 150
Then, we'll subtract 120 from both sides:
2x = 30
Finally, we'll divide both sides by 2:
x = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.