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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
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
104+16x=92+13x ; x=4
104 plus 16 x equals 92 plus 13 x ; x equals 4
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To solve this problem, we need to set up an equation where the number of cans filled by the first machine is equal to the number of cans filled by the second machine.
Let x be the number of minutes it takes for the two machines to have filled the same number of cans.
For the first machine: number of cans filled = 92 + 16x
For the second machine: number of cans filled = 104 + 13x
Setting these two expressions equal to each other, we get:
92 + 16x = 104 + 13x
Now, we can solve this equation to find the value of x.
Subtract 13x from both sides:
92 + 3x = 104
Subtract 92 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Therefore, the two machines will have filled the same number of cans of soup after 4 minutes.
To find out when the two machines will have filled the same number of cans of soup, we need to set up an equation.
Let's assume x is the number of minutes it takes for the machines to fill the same number of cans.
The first machine fills cans at a rate of 16 cans per minute, so the total number of cans it fills in x minutes is 16x.
The second machine fills cans at a rate of 13 cans per minute, so the total number of cans it fills in x minutes is 13x.
Therefore, the equation to represent the situation is:
92 + 16x = 104 + 13x
To solve the equation, we need to isolate the variable x.
Subtract 13x from both sides of the equation:
92 + 16x - 13x = 104 + 13x - 13x
3x = 12
Divide both sides of the equation by 3:
(3x)/3 = 12/3
x = 4
Therefore, the two machines will have filled the same number of cans of soup after 4 minutes.
To solve this problem, we need to set up an equation to represent the situation. Let's represent the number of minutes as "x".
For the first machine, the equation would be 92 + 16x, where 92 is the number of cans filled initially and 16x is the number of cans filled by the machine in x minutes.
For the second machine, the equation would be 104 + 13x, where 104 is the number of cans filled initially and 13x is the number of cans filled by the machine in x minutes.
Since we want to find the time when the two machines will have filled the same number of cans, we need to set the two equations equal to each other.
So, we have the equation 92 + 16x = 104 + 13x.
Now we can solve for x by simplifying and isolating the x term.
First, subtract 13x from both sides of the equation:
92 + 16x - 13x = 104 + 13x - 13x
This simplifies to:
92 + 3x = 104
Next, subtract 92 from both sides of the equation:
92 + 3x - 92 = 104 - 92
This simplifies to:
3x = 12
Finally, divide both sides of the equation by 3 to solve for x:
3x/3 = 12/3
This simplifies to:
x = 4
Therefore, the two machines will have filled the same number of cans of soup after 4 minutes.