Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Four percent of the panels from Plant A and 3% of the panels from Plant B were defective. How many panels did Plant A produce, if the two plants together produced 880 defective panels?

Let's break down the problem step by step:

Step 1: Let's assume the number of panels produced by Plant B is X.

Step 2: According to the problem, Plant A produced 6000 fewer panels than Plant B did. So the number of panels produced by Plant A is (X - 6000).

Step 3: 4% of the panels from Plant A were defective. This means 4% of (X - 6000) panels were defective, which is (4/100)(X - 6000).

Step 4: 3% of the panels from Plant B were defective. This means 3% of X panels were defective, which is (3/100)X.

Step 5: The total number of defective panels produced by both plants is given as 880. So we can write the equation:
(4/100)(X - 6000) + (3/100)X = 880

Step 6: Simplifying the equation:
(4/100)X - (24/100) + (3/100)X = 880
(7/100)X - (24/100) = 880

Step 7: Combining like terms and getting rid of fractions:
(7X - 2400)/100 = 880

Step 8: Cross-multiplying:
7X - 2400 = 880 * 100
7X - 2400 = 88000

Step 9: Simplifying the equation:
7X = 88000 + 2400
7X = 90400

Step 10: Dividing both sides by 7 to solve for X:
X = 90400 / 7

Step 11: Calculating X:
X = 12914.29

Step 12: Since the number of panels must be a whole number, we can round X down to the nearest whole number since we can't produce a fraction of a panel:
X ≈ 12914

Step 13: Now that we know the number of panels produced by Plant B is approximately 12914, we can calculate the number of panels produced by Plant A:
(X - 6000) = (12914 - 6000) = 6914

Therefore, Plant A produced approximately 6914 panels.

To find out how many panels Plant A produced, we need to set up equations based on the given information.

Let's say the number of panels produced by Plant B is represented by "x".
According to the problem, Plant A produced 6000 fewer panels than Plant B. So, the number of panels produced by Plant A can be represented as "x - 6000".

Now, we know that 4% of the panels from Plant A were defective, and 3% of the panels from Plant B were defective. We are given that the total number of defective panels produced by both plants is 880.

So, we can set up the following equation:
0.04(x - 6000) + 0.03x = 880

Now, we can solve this equation to find the value of "x", which represents the number of panels produced by Plant B.

0.04x - 240 + 0.03x = 880
0.07x - 240 = 880
0.07x = 1120
x = 1120 / 0.07
x = 16000

Therefore, Plant B produced 16000 panels.

To find out how many panels Plant A produced, we substitute the value of x back into the expression for Plant A's production: x - 6000.

Plant A's production = 16000 - 6000
Plant A's production = 10000

Therefore, Plant A produced 10000 panels.

number from A ---- x

number from Bx+6000

solve for x:

.04x + .03(x+6000) = 880

632