Linear Equations in Real-World Scenarios Quick Check
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)
◎ 92+ 162= 104+ 132:2=4
• 104 + 16x = 92+130:1=4
0 92 - 16 = 104 - 132; 2 = -4
O 92 + 16+ = 104+130:2=6
The correct equation to represent the situation is:
92 + 16x = 104 + 13x
To find the value of x, you need to solve for x.
92 + 16x = 104 + 13x
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 solve this problem, we need to determine when the two machines will have filled the same number of cans of soup. Let's represent the time in minutes as 'x'.
The first machine fills cans at a rate of 16 cans per minute. So, the total number of cans filled by the first machine can be calculated as 16x.
The second machine fills cans at a rate of 13 cans per minute. So, the total number of cans filled by the second machine can be calculated as 13x.
We can set up the following equation to find when the two machines will have filled the same number of cans of soup:
16x = 13x
Now, let's solve this equation step by step:
16x - 13x = 0
3x = 0
Dividing both sides by 3, we get:
x = 0
Therefore, the two machines will have filled the same number of cans of soup at x = 0. This means that they would have filled the same number of cans when no time has passed.
To write and solve an equation to show when the two machines will have filled the same number of cans of soup, let's first define some variables.
Let x be the number of minutes it takes for the first machine to fill cans of soup.
Then, the number of cans filled by the first machine would be 16x.
Similarly, the number of cans filled by the second machine would be 13x.
To find when the two machines will have filled the same number of cans, we can set up an equation:
16x = 13x
Now, let's solve the equation:
16x - 13x = 0
3x = 0
Dividing both sides by 3:
x = 0
Hence, the two machines will have filled the same number of cans of soup after 0 minutes.