plant a produced 8000 fewer panels than plant b, 4 % 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 660 defective panels?
6000
panels produced by plant A --- x
panels produced by plant B = x+8000
defective from A = .04x
defective from B = .03(x+8000)
solve for x:
.04x + .03(x+8000) = 660
(I would get that "caps lock" key fixed on your device)
Let's start by setting up some equations to represent the given information:
Let's assume the number of panels produced by Plant A is x.
The number of panels produced by Plant B is (x + 8000) since Plant A produces 8000 fewer panels than Plant B.
From the given information, we know that 4% of the panels from Plant A and 3% of the panels from Plant B were defective. We can use this information to set up the following equations:
0.04x = number of defective panels from Plant A
0.03(x + 8000) = number of defective panels from Plant B
We are also given that the two plants together produced 660 defective panels. Therefore:
0.04x + 0.03(x + 8000) = 660
Now, let's solve this equation to find the value of x:
0.04x + 0.03x + 240 = 660
0.07x = 420
x = 420 / 0.07
x ≈ 6000
Therefore, Plant A produced approximately 6000 panels.
To solve this problem, we'll need to use some algebraic equations. Let's break down the information given:
1. Plant A produced 8000 fewer panels than Plant B.
Let's represent the number of panels produced by Plant B as "B". So the number of panels produced by Plant A would be "B - 8000".
2. 4% of the panels from Plant A and 3% of the panels from Plant B were defective.
We'll need to work with percentages, so let's convert them to decimals. 4% is equal to 0.04, and 3% is equal to 0.03.
The number of defective panels from Plant A would be 0.04 * (B - 8000).
The number of defective panels from Plant B would be 0.03 * B.
3. The two plants together produced 660 defective panels.
The total number of defective panels from both plants would be the sum of the defective panels from Plant A and Plant B. So the equation would be:
0.04 * (B - 8000) + 0.03 * B = 660
Now, let's solve the equation to find the value of B, which represents the number of panels produced by Plant B:
0.04B - 320 + 0.03B = 660
0.07B - 320 = 660
0.07B = 980
B = 14000
So, Plant B produced 14,000 panels.
To find the number of panels produced by Plant A, we'll substitute the value of B into the equation B - 8000:
A = 14000 - 8000
A = 6000
Therefore, Plant A produced 6,000 panels.