Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity, and sells 5 gallons of popcorn per hour. Write an equation to show when the two popcorn machines will have the same amount of popcorn left. Use x as your variable.(1 point)
For Movie Theatre A, the amount of popcorn left (in gallons) after x hours can be represented by the equation 100 - 3x.
For Movie Theatre B, the amount of popcorn left (in gallons) after x hours can be represented by the equation 150 - 5x.
Setting these two equations equal to each other gives:
100 - 3x = 150 - 5x
An ice cream shop makes vanilla and chocolate ice cream. The vanilla ice cream machine has a 180-cup capacity, and it sells 20 cups per day. The chocolate ice cream machine has a 140-cup capacity, and it sells 16 cups per day. Write and solve an equation to show when the two machines will have the same amount of ice cream left.(1 point)
Responses
For the vanilla ice cream machine, the amount of ice cream left (in cups) after x days can be represented by the equation 180 - 20x.
For the chocolate ice cream machine, the amount of ice cream left (in cups) after x days can be represented by the equation 140 - 16x.
Setting these two equations equal to each other gives:
180 - 20x = 140 - 16x
Simplifying the equation further:
4x = 40
Dividing both sides by 4:
x = 10
Therefore, the two machines will have the same amount of ice cream left after 10 days.
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)
For Movie Theatre A, the amount of popcorn left (in gallons) after x hours can be represented by the equation 120 - 7x.
For Movie Theatre B, the amount of popcorn left (in gallons) after x hours can be represented by the equation 150 - 9x.
Setting these two equations equal to each other gives:
120 - 7x = 150 - 9x
Adding 9x and subtracting 120 from both sides:
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.
Write an equation and interpret the solution to the following problem: Rental car A has a rate of an initial $100, plus $10 per day. Rental car B has a rate of an initial $50, plus $20 per day. After how many days are the rental car prices equal?(1 point)
Responses
Let's denote the number of days as x.
The equation for Rental Car A can be represented as: 100 + 10x.
The equation for Rental Car B can be represented as: 50 + 20x.
Setting these two equations equal to each other gives: 100 + 10x = 50 + 20x.
Subtracting 10x from both sides to isolate the x term gives: 100 = 50 + 10x.
Subtracting 50 from both sides gives: 50 = 10x.
Dividing both sides by 10 gives: 5 = x.
Therefore, the rental car prices are equal after 5 days.