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
210−12x=180−15x
210 minus 12 x equals 180 minus 15 x
12x−210=15x−180
12 x minus 210 equals 15 x minus 180
12x+180=15x+210
Linear Equations in Real-World Scenarios Quick Check
2 of 52 of 5 Items
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
150+3x=100+5x
150 plus 3 x equals 100 plus 5 x
100+3x=150+5x
100 plus 3 x equals 150 plus 5 x
3x−100=5x−150
3 x minus 100 equals 5 x minus 150
100−3x=150−5x
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+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
Two machines at a factory are filling cans of soup. One machine has filled 92 cans of soup. It fills cans at a rate of 16 cans per minute. The second machine has filled 104 cans of soup. It fills cans at a rate of 13 cans per minute. Write and solve an equation to show when the two machines will have filled the same number of cans of soup.(1 point)
Responses
104+16x=92+13x ; x=4
104 plus 16 x equals 92 plus 13 x ; x equals 4
92−16x=104−13x ; x=−4
92 minus 16 x equals 104 minus 13 x ; x equals negative 4
92+16x=104+13x ; x=4
92 plus 16 x equals 104 plus 13 x ; x equals 4
92+16x=104+13x ; x=6
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=−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