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?? After how many minutes
Let's denote the time in minutes as "t".
At time t, the first vat will have 6t gallons of liquid (since it is being filled at a rate of 6 gallons per minute).
Meanwhile, the second vat will have 28 + 4t gallons of liquid (since it already contains 28 gallons and is being filled at a rate of 4 gallons per minute).
To find the time when the two vats have the same amount of liquid, we can set up the following equation:
6t = 28 + 4t
Simplifying this equation, we get:
2t = 28
Dividing both sides by 2, we get:
t = 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 $30 per month, and $4 per visit. How many visits would make the cost of both plans the same?
Let's assume the number of visits per month as "v".
For the first plan, the cost per month is fixed at $30. Additionally, the cost per visit is $4. Therefore, the total cost for the first plan is:
Total cost for first plan = $30 + $4v
For the second plan, each visit costs $10. Therefore, the total cost for the second plan is simply the cost per visit multiplied by the number of visits:
Total cost for second plan = $10v
To find the number of visits that would make the cost of both plans the same, we can set up the following equation:
$30 + $4v = $10v
Subtracting $4v from both sides of the equation, we get:
$30 = $6v
To isolate "v", we divide both sides of the equation by $6:
$30 / $6 = v
5 = v
Therefore, the cost of both plans would be the same if there are 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 cans of soup. Use x as your variable.
Let's denote the time in minutes as "x".
The first machine fills cans at a rate of 15 cans per minute, so the number of cans it fills after x minutes would be 15x.
The second machine fills cans at a rate of 12 cans per minute, so the number of cans it fills after x minutes would be 12x.
To find when the two machines will have filled the same number of cans, we can set up the following equation:
180 + 15x = 210 + 12x
Here, 180 is the initial number of cans filled by the first machine, 210 is the initial number of cans filled by the second machine, and 15x and 12x represent the additional cans filled by the first and second machines, respectively, after x minutes.
Simplifying this equation, we get:
15x - 12x = 210 - 180
3x = 30
Dividing both sides by 3, we get:
x = 10
Therefore, the two machines will have filled the same number of cans after 10 minutes.
The answers are
210-12x=180-15x
12x-210=15x-180
12x+210=15x+180
12x+180=15x+210
Which is correct??
Apologies for the confusion. The correct equation should be:
180 + 15x = 210 + 12x
Please disregard the previous equations and calculations provided.
So the answer would be 12x+210=15x+180
That is correct. The equation to represent when the two machines will have filled the same number of cans is:
12x + 210 = 15x + 180