The equation to show when the two vats will have an equal amount of liquid can be represented as:
6x = 10 + 4x
Simplifying the equation:
2x = 10
Dividing both sides by 2:
x = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
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)
what is the anwser
23 answers
wrong
Apologies for the mistake. Let's try again.
The equation to show when the two vats will have an equal amount of liquid can be represented as:
6x = 10 + 4x
To solve for x, we need to isolate the x term:
6x - 4x = 10
2x = 10
Divide both sides by 2:
x = 10/2
x = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
The equation to show when the two vats will have an equal amount of liquid can be represented as:
6x = 10 + 4x
To solve for x, we need to isolate the x term:
6x - 4x = 10
2x = 10
Divide both sides by 2:
x = 10/2
x = 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 x as your variable.(1 point)
For the first plan, the cost is $8 per visit, so the equation to represent the cost for the first plan based on the number of visits (x) would be:
Cost of first plan = 8x
For the second plan, the cost is $40 per month and $2 per visit. Let's assume the number of visits per month is y. The equation to represent the cost for the second plan would be:
Cost of second plan = 40 + 2y
To find the number of visits per month (y) that it would take for the two plans to be equal, we need to set the two equations equal to each other:
8x = 40 + 2y
This equation shows the number of visits per month (y) that it would take for the two plans to be equal, given a certain number of visits (x) for the first plan.
Cost of first plan = 8x
For the second plan, the cost is $40 per month and $2 per visit. Let's assume the number of visits per month is y. The equation to represent the cost for the second plan would be:
Cost of second plan = 40 + 2y
To find the number of visits per month (y) that it would take for the two plans to be equal, we need to set the two equations equal to each other:
8x = 40 + 2y
This equation shows the number of visits per month (y) that it would take for the two plans to be equal, given a certain number of visits (x) for the first plan.
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
minutes.
To determine when the two vats will have the same amount of liquid, we can set up an equation:
Let x represent the number of minutes it takes for the vats to have the same amount of liquid.
For the first vat, which starts empty and fills at a rate of 6 gallons per minute, the amount of liquid in the vat after x minutes is 6x gallons.
For the second vat, which already contains 28 gallons and fills at a rate of 4 gallons per minute, the amount of liquid in the vat after x minutes is 28 + 4x gallons.
To find the point when the two vats have the same amount of liquid, we can set up an equation:
6x = 28 + 4x
Subtracting 4x from both sides:
6x - 4x = 28
Simplifying:
2x = 28
Dividing both sides by 2:
x = 14
Therefore, the two vats will have the same amount of liquid after 14 minutes.
Let x represent the number of minutes it takes for the vats to have the same amount of liquid.
For the first vat, which starts empty and fills at a rate of 6 gallons per minute, the amount of liquid in the vat after x minutes is 6x gallons.
For the second vat, which already contains 28 gallons and fills at a rate of 4 gallons per minute, the amount of liquid in the vat after x minutes is 28 + 4x gallons.
To find the point when the two vats have the same amount of liquid, we can set up an equation:
6x = 28 + 4x
Subtracting 4x from both sides:
6x - 4x = 28
Simplifying:
2x = 28
Dividing both sides by 2:
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 plans would cost the same at
visits.
To determine the number of visits that would make the cost of both plans equal, we can set up an equation.
Let x represent the number of visits.
For the first plan, the cost per visit is $10, so the total cost for x visits would be 10x.
For the second plan, the cost per month is $30 and $4 per visit. So, the total cost for x visits would be 30 + 4x.
Setting up the equation:
10x = 30 + 4x
Subtracting 4x from both sides:
10x - 4x = 30
Simplifying:
6x = 30
Dividing both sides by 6:
x = 5
Therefore, the two plans would cost the same when there are 5 visits.
Let x represent the number of visits.
For the first plan, the cost per visit is $10, so the total cost for x visits would be 10x.
For the second plan, the cost per month is $30 and $4 per visit. So, the total cost for x visits would be 30 + 4x.
Setting up the equation:
10x = 30 + 4x
Subtracting 4x from both sides:
10x - 4x = 30
Simplifying:
6x = 30
Dividing both sides by 6:
x = 5
Therefore, the two plans would cost the same when there are 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?(1 point)
miles
miles
To determine when bike A and bike B will be the same distance from the starting point, we can set up an equation.
Let x represent the number of miles they both traveled from the starting point.
For bike A, the distance traveled is 50 + x miles.
For bike B, the distance traveled is 100 + x miles.
To find when the two distances are equal, we can set up an equation:
50 + x = 100 + x
Subtracting x from both sides:
50 = 100
This equation is not true for any value of x, which means that bike A and bike B will never be the same distance from the starting point.
Let x represent the number of miles they both traveled from the starting point.
For bike A, the distance traveled is 50 + x miles.
For bike B, the distance traveled is 100 + x miles.
To find when the two distances are equal, we can set up an equation:
50 + x = 100 + x
Subtracting x from both sides:
50 = 100
This equation is not true for any value of x, which means that bike A and bike B will never be the same distance from the starting 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
12x+210=15x+180
12 x plus 210 equals 15 x plus 180
12x+180=15x+210
12 x plus 180 equals 15 x plus 210
12x−210=15x−180
12 x minus 210 equals 15 x minus 180
210−12x=180−15x
Responses
12x+210=15x+180
12 x plus 210 equals 15 x plus 180
12x+180=15x+210
12 x plus 180 equals 15 x plus 210
12x−210=15x−180
12 x minus 210 equals 15 x minus 180
210−12x=180−15x
The correct equation to show when the two machines will have filled the same number of cans of soup is:
12x + 210 = 15x + 180
12x + 210 = 15x + 180
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
3x−100=5x−150
3 x minus 100 equals 5 x minus 150
100−3x=150−5x
100 minus 3 x equals 150 minus 5 x
100+3x=150+5x
100 plus 3 x equals 150 plus 5 x
150+3x=100+5x
150 plus 3 x equals 100 plus 5 x
Responses
3x−100=5x−150
3 x minus 100 equals 5 x minus 150
100−3x=150−5x
100 minus 3 x equals 150 minus 5 x
100+3x=150+5x
100 plus 3 x equals 150 plus 5 x
150+3x=100+5x
150 plus 3 x equals 100 plus 5 x
The correct equation to show when the two popcorn machines will have the same amount of popcorn left is:
3x - 100 = 5x - 150
3x - 100 = 5x - 150
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
180−20x=140−16x ; x=10
180 minus 20 x equals 140 minus 16 x ; x equals 10
180+16x=140+20x ; x=−10
180 plus 16 x equals 140 plus 20 x ; x equals negative 10
180−20x=140−16x ; x=20
180 minus 20 x equals 140 minus 16 x ; x equals 20
140+16x=180+20x ; x=10
Responses
180−20x=140−16x ; x=10
180 minus 20 x equals 140 minus 16 x ; x equals 10
180+16x=140+20x ; x=−10
180 plus 16 x equals 140 plus 20 x ; x equals negative 10
180−20x=140−16x ; x=20
180 minus 20 x equals 140 minus 16 x ; x equals 20
140+16x=180+20x ; x=10
The correct equation to show when the two machines will have the same amount of ice cream left is:
180 - 20x = 140 - 16x
To solve this equation, we'll start by simplifying:
-20x + 16x = 140 - 180
Combine like terms:
-4x = -40
To isolate x, we'll divide both sides by -4:
x = (-40) / (-4)
Simplifying:
x = 10
Therefore, the two machines will have the same amount of ice cream left after 10 days.
180 - 20x = 140 - 16x
To solve this equation, we'll start by simplifying:
-20x + 16x = 140 - 180
Combine like terms:
-4x = -40
To isolate x, we'll divide both sides by -4:
x = (-40) / (-4)
Simplifying:
x = 10
Therefore, the two machines will have the same amount of ice cream left after 10 days.
what is the anwser
The answer is that the two machines will have the same amount of ice cream left after 10 days.
Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.(1 point)
Responses
120x−7=150x−9 ; x=15
120 x minus 7 equals 150 x minus 9 ; x equals 15
120−7x=150−9x ; x=15
120 minus 7 x equals 150 minus 9 x ; x equals 15
120−7x=150−9x ; x=10
120 minus 7 x equals 150 minus 9 x ; x equals 10
120+7x=150+9x ; x=−15
Responses
120x−7=150x−9 ; x=15
120 x minus 7 equals 150 x minus 9 ; x equals 15
120−7x=150−9x ; x=15
120 minus 7 x equals 150 minus 9 x ; x equals 15
120−7x=150−9x ; x=10
120 minus 7 x equals 150 minus 9 x ; x equals 10
120+7x=150+9x ; x=−15
The correct equation to show when the two popcorn machines will have the same amount of popcorn left is:
120x - 7 = 150x - 9
To solve this equation, let's simplify and isolate the x term:
-7 + 9 = 150x - 120x
2 = 30x
Divide both sides by 30:
2/30 = x
Simplifying:
1/15 = x
Therefore, the two popcorn machines will have the same amount of popcorn left after 1/15 of an hour or approximately 4 minutes.
120x - 7 = 150x - 9
To solve this equation, let's simplify and isolate the x term:
-7 + 9 = 150x - 120x
2 = 30x
Divide both sides by 30:
2/30 = x
Simplifying:
1/15 = x
Therefore, the two popcorn machines will have the same amount of popcorn left after 1/15 of an hour or approximately 4 minutes.
Write an equation and interpret the solution to the following problem: Rental car A has a rate of an initial $100, plus $10 per day. Rental car B has a rate of an initial $50, plus $20 per day. After how many days are the rental car prices equal?(1 point)
Responses
50x+20=100x+10; x=5; after 5 days the prices are equal
50 x plus 20 equals 100 x plus 10 ; x equals 5 ; after 5 days the prices are equal
20x−50=10x−100; x=−5; after 5 days the prices are equal
20 x minus 50 equals 10 x minus 100 ; x equals negative 5 ; after 5 days the prices are equal
50+20x=100x+10; x=1; after 1 day the prices are equal
50 plus 20 x equals 100 x plus 10 ; x equals 1 ; after 1 day the prices are equal
50+20x=100+10x; x=5; after 5 days the prices are equal
Responses
50x+20=100x+10; x=5; after 5 days the prices are equal
50 x plus 20 equals 100 x plus 10 ; x equals 5 ; after 5 days the prices are equal
20x−50=10x−100; x=−5; after 5 days the prices are equal
20 x minus 50 equals 10 x minus 100 ; x equals negative 5 ; after 5 days the prices are equal
50+20x=100x+10; x=1; after 1 day the prices are equal
50 plus 20 x equals 100 x plus 10 ; x equals 1 ; after 1 day the prices are equal
50+20x=100+10x; x=5; after 5 days the prices are equal
The correct equation to show when the rental car prices are equal is:
50 + 20x = 100 + 10x
To solve this equation, we'll start by simplifying and isolating the x term:
20x - 10x = 100 - 50
10x = 50
Divide both sides by 10:
x = 5
Therefore, after 5 days, the rental car prices for rental car A and rental car B will be equal.
50 + 20x = 100 + 10x
To solve this equation, we'll start by simplifying and isolating the x term:
20x - 10x = 100 - 50
10x = 50
Divide both sides by 10:
x = 5
Therefore, after 5 days, the rental car prices for rental car A and rental car B will be equal.
1 answer