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)
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
210−12x=180−15x
210 minus 12 x equals 180 minus 15 x
12x−210=15x−180
12 x minus 210 equals 15 x minus 180
12x+180=15x+210
12 x plus 180 equals 15 x plus 210
12x+210=15x+180
Let x be the number of minutes it takes for the machines to have filled the same number of cans of soup.
The first machine fills cans at a rate of 15 per minute, so in x minutes it will have filled 15x cans of soup.
The second machine fills cans at a rate of 12 per minute, so in x minutes it will have filled 12x cans of soup.
To find when the two machines will have filled the same number of cans of soup, we set 15x equal to 12x:
15x = 12x
12x + 210 = 15x + 180
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 is already filled with 10 gallons, and it is continuing to fill at a rate of 4 gallons per minute. Write an equation to show when the two vats will have an equal amount of liquid. Use x as your variable. (1 point)
Let x be the number of minutes it takes for the two vats to have an equal amount of liquid.
The first vat is being filled at a rate of 6 gallons per minute, so in x minutes it will have 6x gallons of liquid.
The second vat already has 10 gallons of liquid and is filling at a rate of 4 gallons per minute, so in x minutes it will have 4x + 10 gallons of liquid.
To find when the two vats will have an equal amount of liquid, we set 6x equal to 4x + 10:
6x = 4x + 10
A yoga studio has two participation plans. For the first plan, the cost is $8 per visit. For the second plan, the cost is $40 per month, and $2 per visit. Write an equation to show the number of visits per month that it would take for the two plans to be equal. Use x as your variable.(1 point)
Let x be the number of visits per month.
For the first plan, the cost is $8 per visit, so the total cost would be 8x.
For the second plan, the cost is $40 per month and $2 per visit. So the total cost would be 40 + 2x.
To find when the two plans are equal, we set 8x equal to 40 + 2x:
8x = 40 + 2x
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)
Let x be the number of days.
The vanilla milkshake machine has a 300-cup capacity and sells 15 cups per day. So, the amount of milkshake left after x days on the vanilla machine is 300 - 15x.
The chocolate milkshake machine has a 280-cup capacity and sells 20 cups per day. So, the amount of milkshake left after x days on the chocolate machine is 280 - 20x.
To find when the two machines will have the same amount of milkshake left, we set 300 - 15x equal to 280 - 20x:
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.