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 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 minus 7 x equals 150 minus 9 x ; 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

Answer 1

To find when the two popcorn machines will have the same amount of popcorn left, we can set up an equation based on their capacities and sales rates.

Let \( x \) be the number of hours after which we are measuring the amount of popcorn left.

For Movie Theatre A:

• Initial popcorn: 120 gallons
• Popcorn sold: 7 gallons per hour
• Amount left after \( x \) hours: \( 120 - 7x \)

For Movie Theatre B:

• Initial popcorn: 150 gallons
• Popcorn sold: 9 gallons per hour
• Amount left after \( x \) hours: \( 150 - 9x \)

Now we can set the two expressions equal to each other:

\[ 120 - 7x = 150 - 9x \]

Now, we will solve for \( x \):

1. Start by adding \( 9x \) to both sides:

\[ 120 - 7x + 9x = 150 \]

2. This simplifies to:

\[ 120 + 2x = 150 \]

3. Next, subtract 120 from both sides:

\[ 2x = 30 \]

4. Finally, divide by 2:

\[ x = 15 \]

Thus, the solution to the equation is \( x = 15 \).

This means that in 15 hours, both popcorn machines will have the same amount of popcorn left.