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 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
92+16x=104+13x ; x=6
92 plus 16 x equals 104 plus 13 x ; x equals 6
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
None of the provided responses are correct.
The correct equation to represent the scenario is:
92 + 16x = 104 + 13x, where x represents the number of minutes it takes for the two machines to have filled the same number of cans.
To solve for x, subtract 13x from both sides:
92 + 3x = 104
Then, subtract 92 from both sides:
3x = 12
Finally, divide both sides by 3:
x = 4
So, the correct answer is option:
92+16x=104+13x ; x=4