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.
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Question
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+180=15x+210
12 x plus 180 equals 15 x plus 210
12x−210=15x−180
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Question
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
100+3x=150+5x
100 plus 3 x equals 150 plus 5 x
150+3x=100+5x
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Question
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+16x=140+20x ; x=−10
180 plus 16 x equals 140 plus 20 x ; x equals negative 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
140+16x=180+20x ; x=10
140 plus 16 x equals 180 plus 20 x ; x equals 10
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=−15
120 plus 7 x equals 150 plus 9 x ; x equals negative 15
120−7x=150−9x ; x=10
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Question
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
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
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=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
Let x represent the number of minutes it takes for the two machines to have filled the same number of cans of soup.
The first machine fills cans at a rate of 15 per minute, so after x minutes it will have filled 15x cans of soup.
The second machine fills cans at a rate of 12 per minute, so after x minutes it will have filled 12x cans of soup.
Setting these two expressions equal to each other, we can write the equation 15x = 12x to show when the two machines will have filled the same number of cans of soup.