Linear Equations in Real-World Scenarios Quick Check
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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
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
210 minus 12 x equals 180 minus 15 x
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
150+3x=100+5x
150 plus 3 x equals 100 plus 5 x
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
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+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
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180 minus 20 x equals 140 minus 16 x ; x equals 20
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 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
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
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
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
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 5 ; after 5 days the prices are equal
To write an equation to show when the two machines will have filled the same number of cans of soup, we can set up an equation based on the information given.
Let's assign x as the time in minutes when the two machines will have filled the same number of cans of soup.
The first machine has already filled 180 cans of soup and fills cans at a rate of 15 per minute. So, the cans filled by the first machine can be represented as 15x + 180.
The second machine has already filled 210 cans of soup and fills cans at a rate of 12 per minute. So, the cans filled by the second machine can be represented as 12x + 210.
Since we want to find the time when the two machines will have filled the same number of cans, we can set these two expressions equal to each other:
15x + 180 = 12x + 210
So, the correct equation here is:
12x + 180 = 15x + 210