100 gallon compactly and sells 3 gallons of popcorn per hour movie theatre b has 150 compaction and sells 5 gallons per hour write equation showing when the two popcorn machines have the same amount left
Let's represent the number of hours passed as "t".
For movie theatre A:
Initial amount of popcorn = 100 gallons
Amount of popcorn sold after t hours = 3t gallons
Amount of popcorn left = 100 - 3t gallons
For movie theatre B:
Initial amount of popcorn = 150 gallons
Amount of popcorn sold after t hours = 5t gallons
Amount of popcorn left = 150 - 5t gallons
To find the time when both movie theatres have the same amount of popcorn left, we need to equate the expressions for the amount of popcorn left and solve for t:
100 - 3t = 150 - 5t
Subtracting 100 and adding 5t to both sides:
-3t + 5t = 150 - 100
Simplifying:
2t = 50
Dividing by 2:
t = 25
Therefore, the two popcorn machines will have the same amount of popcorn left after 25 hours.
An ice cream shop makes vanilla and chocolate ice cream the vanilla I cream machine has 140 cup compactor and it sells 16 cups per day write an equation to show that they will have the same amount of ice cream left
Let's represent the number of days passed as "t".
For the vanilla ice cream machine:
Initial amount of vanilla ice cream cups = 140 cups
Amount of vanilla ice cream cups sold after t days = 16t cups
Amount of vanilla ice cream cups left = 140 - 16t cups
For the chocolate ice cream machine (assuming it has the same initial amount and sales rate):
Initial amount of chocolate ice cream cups = 140 cups
Amount of chocolate ice cream cups sold after t days = 16t cups
Amount of chocolate ice cream cups left = 140 - 16t cups
To find the time when both ice cream machines have the same amount of ice cream left, we need to equate the expressions for the amount of ice cream cups left and solve for t:
140 - 16t = 140 - 16t
This equation is already in simplified form and tells us that the amount of vanilla and chocolate ice cream cups left will always be the same, regardless of the number of days passed.
Movie theatre has popcorn machine with 120 gallon vopacity it sells 7 gallons per hour movie b has a machine with 150 gallons and t sells 9 gallons per hour write and solve an equation to show how much popcorn will be left
Let's represent the number of hours passed as "t".
For movie theatre A:
Initial amount of popcorn = 120 gallons
Amount of popcorn sold after t hours = 7t gallons
Amount of popcorn left = 120 - 7t gallons
For movie theatre B:
Initial amount of popcorn = 150 gallons
Amount of popcorn sold after t hours = 9t gallons
Amount of popcorn left = 150 - 9t gallons
To find the amount of popcorn left, we need to equate the expressions for the amount of popcorn left in both movie theatres and solve for t:
120 - 7t = 150 - 9t
Adding 7t to both sides:
120 = 150 - 2t
Subtracting 150 from both sides:
-30 = -2t
Dividing by -2 (which is equivalent to multiplying by -1/2):
t = 15
Therefore, after 15 hours, both movie theatres will have the same amount of popcorn left. To find the amount of popcorn left at that time, substitute t = 15 into either expression for the amount of popcorn left.
Write an equation and interpret the solution to the following to the following rental a has a rate of an initial 100 plus 10 per day rental b uas an rate of 50 plus 20 a day after how many days are the rentals car prices equal
Let's represent the number of days as "d".
For rental A:
Cost of rental A = 100 + 10d dollars
For rental B:
Cost of rental B = 50 + 20d dollars
To find the number of days when the rental car prices are equal, we need to equate the expressions for the cost of rental A and rental B and solve for "d":
100 + 10d = 50 + 20d
Subtracting 10d and 50 from both sides:
50 = 10d
Dividing by 10:
d = 5
Therefore, after 5 days, the rental car prices of both rentals A and B will be equal.