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.

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.

3x−100=5x−150

100+3x=150+5x

100−3x=150−5x

150+3x=100+5x

3x - 100 = 5x - 150

Linear Equations in Real-World Scenarios Quick Check

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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.

180−20x=140−16x ; x=10

180−20x=140−16x ; x=20

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

180+16x=140+20x ; x=−10

180 - 20x = 140 - 16x ; x = 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.

120+7x=150+9x ; x=−15

120−7x=150−9x ; x=10

120x−7=150x−9 ; x=15

120−7x=150−9x ; x=15

120 - 7x = 150 - 9x; x = 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?

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

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

50+20x=100x+10; x=1; after 1 day the prices are equal

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

50 + 20x = 100 + 10x; x = 5; after 5 days the rental car prices are equal.

The correct equation to show when the two machines will have filled the same number of cans of soup is "12x + 210 = 15x + 180".