A diner makes vanilla milkshakes and chocolate milkshakes. The vanilla milkshake machine has a 300-cup capacity, and sells 15 cups per day. The chocolate milkshake machine has a 280-cup capacity, and sells 20 cups per day. Write an equation to show when the two machines will have the same amount of milkshake left. Use x as your variable.(1 point)
The amount of vanilla milkshakes left can be represented by the equation: 300 - 15x.
The amount of chocolate milkshakes left can be represented by the equation: 280 - 20x.
To find when the two machines will have the same amount of milkshake left, set the two equations equal to each other: 300 - 15x = 280 - 20x.
Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?(1 point)
They will have the same amount of liquid after
minutes.
They will have the same amount of liquid after x minutes.
The amount of liquid in the first vat can be represented by the equation: 6x (since it is filling at a rate of 6 gallons per minute).
The amount of liquid in the second vat can be represented by the equation: 28 + 4x (since it already contains 28 gallons and is filling at a rate of 4 gallons per minute).
To find when the two vats will have the same amount of liquid, set the two equations equal to each other: 6x = 28 + 4x.
Simplifying the equation, we get: 2x = 28.
Dividing both sides of the equation by 2, we get: x = 14.
Therefore, the two vats will have the same amount of liquid after 14 minutes.
A yoga studio has two participation plans. The first plan costs $10 per visit. The second plan costs $30 per month, and $4 per visit. How many visits would make the cost of both plans the same?(1 point)
The plans would cost the same at
visits.
The cost of the first plan is $10 per visit, and the cost of the second plan is $30 per month plus $4 per visit.
Let's represent the number of visits as x.
The cost of the first plan is 10x.
The cost of the second plan is $30 for the month plus $4 for each visit, so it would be 30 + 4x.
To find when the cost of both plans is the same, we set the two equations equal to each other: 10x = 30 + 4x.
Simplifying the equation, we get: 6x = 30.
Dividing both sides of the equation by 6, we get: x = 5.
Therefore, the plans would cost the same at 5 visits.
Two machines at a factory are filling cans of soup. One machine has already filled 180 cans of soup, and fills cans at a rate of 15 per minute. The second machine has already filled 210 cans of soup, and fills cans at a rate of 12 per minute. Write an equation to show when the two machines will have filled the same number of cans of soup. Use x as your variable.(1 point)
Responses
12x+180=15x+210
12 x plus 180 equals 15 x plus 210
12x+210=15x+180
12 x plus 210 equals 15 x plus 180
12x−210=15x−180
12 x minus 210 equals 15 x minus 180
210−12x=180−15x
The equation to show when the two machines will have filled the same number of cans of soup is: 12x + 180 = 15x + 210.
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)
Responses
100+3x=150+5x
100 plus 3 x equals 150 plus 5 x
100−3x=150−5x
100 minus 3 x equals 150 minus 5 x
3x−100=5x−150
3 x minus 100 equals 5 x minus 150
150+3x=100+5x
The equation to show when the two popcorn machines will have the same amount of popcorn left is: 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
180+16x=140+20x ; x=−10
180 plus 16 x equals 140 plus 20 x ; x equals negative 10
140+16x=180+20x ; x=10
140 plus 16 x equals 180 plus 20 x ; x equals 10
180−20x=140−16x ; x=20
180 minus 20 x equals 140 minus 16 x ; x equals 20
180−20x=140−16x ; x=10