Two pumps are filing large vats of liquid. One vat is empty, and the pump is filing 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 a as your variable.
Let a be the number of minutes it takes for the two vats to have an equal amount of liquid.
At a minutes, the empty vat will have been filled with 6a gallons of liquid, and the other vat will have been filled with 10 + 4a gallons of liquid.
Since the two vats have an equal amount of liquid, we can set up the equation:
6a = 10 + 4a
That’s wrong
Apologies for the mistake. Let's correct it.
Let a be the number of minutes it takes for the two vats to have an equal amount of liquid.
At a minutes, the empty vat will have been filled with 6a gallons of liquid, and the other vat will have been filled with 10 + 4a gallons of liquid.
Since the two vats have an equal amount of liquid, we can set up the equation:
6a = 10 + 4a
Simplifying the equation:
6a - 4a = 10
2a = 10
a = 10/2
a = 5
Therefore, it will take 5 minutes for the two vats to have an equal amount of liquid.
Still wrong
Apologies for the confusion. Let me correct the response.
Let a be the number of minutes it takes for the two vats to have an equal amount of liquid.
At a minutes, the empty vat will have been filled with 6a gallons of liquid, and the other vat will have been filled with 10 + 4a gallons of liquid.
Since the two vats have an equal amount of liquid, we can set up the equation:
6a = 10 + 4a
Rewriting the equation to isolate the variable:
6a - 4a = 10
2a = 10
a = 10/2
a = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
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 › as your variable.
Let v be the number of visits per month.
For the first plan, the cost is $8 per visit, so the total cost for v visits would be 8v dollars.
For the second plan, the cost is $40 per month, plus $2 per visit. So the total cost for v visits would be 40 + 2v dollars.
To find the number of visits per month that it would take for the two plans to be equal, we set up the equation:
8v = 40 + 2v
Simplifying the equation:
8v - 2v = 40
6v = 40
v = 40/6
v = 6.66667
Since v represents the number of visits per month, we cannot have a partial visit, so the number of visits required for the two plans to be equal would be 7 visits per month.
Two pumps are filing large vats of liquid. One vat is empty, and the pump is filing 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.
Let x 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, and the other vat will have been filled with 10 + 4x gallons of liquid.
Since the two vats have an equal amount of liquid, we can set up the equation:
6x = 10 + 4x
Simplifying the equation:
6x - 4x = 10
2x = 10
Therefore, the equation that shows when the two vats will have an equal amount of liquid is:
2x = 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.
Let x be the number of visits per month.
For the first plan, the cost is $8 per visit, so the total cost for x visits would be 8x dollars.
For the second plan, the cost is $40 per month, plus $2 per visit. So the total cost for x visits would be 40 + 2x dollars.
To find the number of visits per month that it would take for the two plans to be equal, we set up the equation:
8x = 40 + 2x
Simplifying the equation:
8x - 2x = 40
6x = 40
Therefore, the equation that shows the number of visits per month required for the two plans to be equal is:
6x = 40
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?
Let t be the number of minutes it takes for the two vats to have the same amount of liquid.
At t minutes, the first vat will have been filled with 6t gallons of liquid, and the second vat will have been filled with 28 + 4t gallons of liquid.
Since the two vats have the same amount of liquid, we can set up the equation:
6t = 28 + 4t
To find t, we can solve this equation:
6t - 4t = 28
2t = 28
t = 28/2
t = 14
Therefore, it will take 14 minutes for the two vats to have the same amount of liquid.
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?
Let v be the number of visits.
For the first plan, the cost is $10 per visit, so the total cost would be 10v dollars.
For the second plan, the cost is $30 per month, plus $4 per visit. So the total cost would be 30 + 4v dollars.
To find the number of visits that would make the cost of both plans the same, we can set up the equation:
10v = 30 + 4v
Simplifying the equation:
10v - 4v = 30
6v = 30
v = 30/6
v = 5
Therefore, 5 visits would make the cost of both plans the same.
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 x be the number of miles both bikes have traveled from the starting point.
Bike A is initially 50 miles from the starting point, so its distance from the starting point after x miles would be 50 + x miles.
Bike B is initially 100 miles from the starting point, so its distance from the starting point after x miles would be 100 + x miles.
To find the number of miles at which both bikes are the same distance from the starting point, we can set up the equation:
50 + x = 100 + x
Simplifying the equation:
x = 100 - 50
x = 50
Therefore, after 50 miles, both Bike A and Bike B will be the same distance from the starting point.