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Question
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)
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Let y be the number of minutes it takes for the two vats to have an equal amount of liquid.
At x minutes, the empty vat will have been filled with 6x gallons of liquid.
At x minutes, the filled vat will have 10 + 4x gallons of liquid.
Therefore, the equation is:
6x = 10 + 4x
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.
Let y be the number of visits per month that it would take for the two plans to be equal.
For the first plan, the cost is $8 per visit. Therefore, the total cost for y visits would be 8y.
For the second plan, the cost is $40 per month, and $2 per visit. Therefore, the total cost for y visits would be 40 + 2y.
Therefore, the equation is:
8y = 40 + 2y
3 of 53 of 5 Items
Question
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.
Let t be the number of minutes it takes for the two vats to have the same amount of liquid.
At time t, the empty vat will have been filled with 6t gallons of liquid.
At time t, the filled vat will have 28 + 4t gallons of liquid.
To find the time when the two vats have the same amount of liquid, we can set the two expressions equal to each other:
6t = 28 + 4t
Simplifying the equation:
2t = 28
Dividing both sides by 2:
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 $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
Let x be the number of visits that would make the cost of both plans the same.
For the first plan, the cost is $10 per visit, so the total cost would be 10x.
For the second plan, the cost is $30 per month and $4 per visit. So, the total cost would be 30 + 4x.
To find the number of visits that would make the cost of both plans the same, we can set the two expressions equal to each other:
10x = 30 + 4x
Simplifying the equation:
6x = 30
Dividing both sides by 6:
x = 5
Therefore, the plans would cost the same at 5 visits.
In a bike race, bike A is 50 miles from the starting point and travels 30 miles per hour. Bike B is 100 miles from the starting point and travels 25 miles per hour. After how many miles will bike A and bike B be the same distance from the starting point?
Let d be the number of miles that both bike A and bike B will be from the starting point.
Bike A travels at a speed of 30 miles per hour, so its distance from the starting point after t hours is given by dA = 30t.
Bike B travels at a speed of 25 miles per hour, so its distance from the starting point after t hours is given by dB = 100 - 25t.
To find the number of miles that both bike A and bike B will be from the starting point when their distances are the same, we can set the two expressions equal to each other:
30t = 100 - 25t
Combine like terms:
55t = 100
Divide both sides by 55:
t = 100/55
t ≈ 1.82 hours
To find the number of miles, we can substitute this value of t into either equation. Let's use the equation for bike A:
dA = 30t = 30 * 1.82 ≈ 54.6 miles
Therefore, bike A and bike B will be the same distance from the starting point after approximately 54.6 miles.
To find the time when the two vats will have an equal amount of liquid, we need to set up an equation. Let's denote the time in minutes as x.
The rate at which the first vat is being filled is 6 gallons per minute. Therefore, the amount of liquid in the first vat after x minutes is 6x gallons.
The rate at which the second vat is being filled is 4 gallons per minute. Since the second vat already has 10 gallons, the amount of liquid in the second vat after x minutes is 10 + 4x gallons.
To find the time when the two vats will have an equal amount of liquid, we set the two expressions equal to each other:
6x = 10 + 4x
Now, we can solve for x. Subtract 4x from both sides:
6x - 4x = 10
Simplifying the equation, we have:
2x = 10
Finally, divide both sides by 2:
x = 5
So, the two vats will have an equal amount of liquid after 5 minutes.