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Question
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
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
120−7x=150−9x ; x=15
120 minus 7 x equals 150 minus 9 x ; x equals 15
120x−7=150x−9 ; x=15
120 x minus 7 equals 150 x minus 9 ; x equals 15
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The correct equation to show when the two popcorn machines will have the same amount of popcorn left is:
120 - 7x = 150 - 9x
To solve this equation, we can simplify it by combining like terms:
-7x + 9x = 150 - 120
2x = 30
Divide both sides of the equation by 2 to solve for x:
x = 15
So the correct solution is x = 15. This means that the two popcorn machines will have the same amount of popcorn left after 15 hours.
The correct equation to show when the two popcorn machines will have the same amount of popcorn left is:
120 - 7x = 150 - 9x
To solve this equation, we need to combine like terms:
120 + 2x = 150
Next, we need to isolate the variable:
2x = 150 - 120
2x = 30
Finally, we solve for x by dividing both sides of the equation by 2:
x = 30/2
x = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.
To find the time when the two popcorn machines will have the same amount of popcorn left, we need to set up an equation based on the information given.
Let's assume x represents the number of hours passed.
For Movie Theatre A, the amount of popcorn left can be calculated by subtracting 7x (7 gallons per hour) from the initial capacity of 120 gallons.
For Movie Theatre B, the amount of popcorn left can be calculated by subtracting 9x (9 gallons per hour) from the initial capacity of 150 gallons.
So, the equation will be:
120 - 7x = 150 - 9x
Now, we can solve the equation to find the value of x, which represents the number of hours when both machines will have the same amount of popcorn left.
By simplifying the equation, you can get:
-7x + 9x = 150 - 120
2x = 30
x = 15
Therefore, the correct equation to show when the two popcorn machines will have the same amount of popcorn left is:
120 - 7x = 150 - 9x
And the answer is x = 15, which means after 15 hours both machines will have the same amount of popcorn left.