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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's call the time in minutes when the two vats have the same amount of liquid as "t".

After "t" minutes, the first vat would have a total of 6t gallons of liquid.

After "t" minutes, the second vat would have a total of 28 + 4t gallons of liquid.

To find the time when the two vats have the same amount of liquid, we can set up the equation:

6t = 28 + 4t.

Simplifying the equation, we can subtract 4t from both sides:

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.

Answer 2

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.

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's call the number of visits "x".

For the first plan, the cost would be 10x dollars.

For the second plan, the cost would be 30 dollars per month plus 4 dollars per visit, so the total cost would be 30 + 4x dollars.

To find the number of visits that make the cost of both plans the same, we can set up the equation:

10x = 30 + 4x.

Simplifying the equation, we can subtract 4x from both sides:

6x = 30.

Dividing both sides by 6, we get:

x = 5.

Therefore, the two plans would cost the same after 5 visits.

Answer 4

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

Answer 5

[AI-generated answer — Bot GPT 3.5]

Let's call the number of miles at which bike A and bike B are the same distance from the starting point "x".

For bike A, the distance from the starting point after traveling x miles would be 50 + x miles.

For bike B, the distance from the starting point after traveling x miles would be 100 - x miles.

To find the number of miles at which bike A and bike B are the same distance from the starting point, we can set up the equation:

50 + x = 100 - x.

Simplifying the equation, we can add x to both sides:

2x = 100.

Dividing both sides by 2, we get:

x = 50.

Therefore, bike A and bike B will be the same distance from the starting point after 50 miles.

Answer 6

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 plus 210 equals 15 x plus 180

12x−210=15x−180
12 x minus 210 equals 15 x minus 180

12x+180=15x+210

Answer 7

[AI-generated answer — Bot GPT 3.5]

The correct equation to represent when the two machines will have filled the same number of cans of soup is:

180 + 15x = 210 + 12x.

Answer 8

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

100−3x=150−5x
100 minus 3 x equals 150 minus 5 x

3x−100=5x−150
3 x minus 100 equals 5 x minus 150

150+3x=100+5x
150 plus 3 x equals 100 plus 5 x

100+3x=150+5x

Answer 9

[AI-generated answer — Bot GPT 3.5]

The correct equation to represent when the two popcorn machines will have the same amount of popcorn left is:

100 + 3x = 150 + 5x.

Answer 10

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

140+16x=180+20x ; x=10
140 plus 16 x equals 180 plus 20 x ; x equals 10

180−20x=140−16x ; x=10
180 minus 20 x equals 140 minus 16 x ; x equals 10

180−20x=140−16x ; x=20
180 minus 20 x equals 140 minus 16 x ; x equals 20

180+16x=140+20x ; x=−10

Answer 11

[AI-generated answer — Bot GPT 3.5]

The correct equation to represent when the two ice cream machines will have the same amount of ice cream left is:

180 - 20x = 140 - 16x.

To solve the equation, we can subtract 140 from both sides:

180 - 140 - 20x = 140 - 140 - 16x,

40 - 20x = -16x.

Next, we can add 20x to both sides:

40 - 20x + 20x = -16x + 20x,

40 = 4x.

Finally, we can divide both sides by 4 to isolate x:

40 / 4 = 4x / 4,

10 = x.

Therefore, the two ice cream machines will have the same amount of ice cream left after 10 days.

Answer 12

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

120+7x=150+9x ; x=−15
120 plus 7 x equals 150 plus 9 x ; x equals negative 15

120x−7=150x−9 ; x=15
120 x minus 7 equals 150 x minus 9 ; 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

Answer 13

[AI-generated answer — Bot GPT 3.5]

The correct equation to represent when the two popcorn machines will have the same amount of popcorn left is:

120 - 7x = 150 - 9x.

To solve the equation, we can add 9x to both sides:

120 - 7x + 9x = 150 - 9x + 9x,

2x = 150 - 120,

2x = 30.

Finally, we can divide both sides by 2 to isolate x:

2x / 2 = 30 / 2,

x = 15.

Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.

Answer 14

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

50+20x=100+10x; x=5; after 5 days the prices are equal
50 plus 20 x equals 100 plus 10 x ; x equals 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

20x−50=10x−100; x=−5; after 5 days the prices are equal

Answer 15

[AI-generated answer — Bot GPT 3.5]

The correct equation to represent the problem is:

50 + 20x = 100x + 10.

To solve the equation, we can subtract 10x from both sides:

50 + 20x - 10x = 100x + 10 - 10x,

50 + 10x = 100,

Then, we can subtract 50 from both sides:

50 + 10x - 50 = 100 - 50,

10x = 50.

Finally, we can divide both sides by 10 to isolate x:

10x / 10 = 50 / 10,

x = 5.

Therefore, the rental car prices will be equal after 5 days.