Two factory plants are making TV panels. Yesterday, Plant A produced
9000
panels. Ten percent of the panels from Plant A and
3%
of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was
6%
?
To find the number of panels produced by Plant B, we need to know the total number of defective panels produced by both plants.
Let's assume the number of panels produced by Plant B is x.
The number of defective panels produced by Plant A is 10% of 9000, which is (10/100) * 9000 = 900.
The number of defective panels produced by Plant B is 3% of x, which is (3/100) * x = 0.03x.
The total number of defective panels from both plants is given as 6% of the total number of panels produced, which is (6/100) * (9000 + x) = 0.06 * (9000 + x).
Now we can set up an equation to solve for x:
900 + 0.03x = 0.06 * (9000 + x)
Simplifying the equation:
900 + 0.03x = 540 + 0.06x
0.03x - 0.06x = 540 - 900
-0.03x = -360
Dividing both sides of the equation by -0.03, we get:
x = -360 / -0.03
x = 12000
Therefore, Plant B produced 12000 panels.
To solve this problem, we can set up an equation based on the information given.
Let's assume that Plant A produced x panels yesterday, and Plant B produced y panels.
From the given information, we know that 10% of Plant A's panels and 3% of Plant B's panels were defective. This means the number of defective panels from Plant A is 0.10x, and the number of defective panels from Plant B is 0.03y.
The overall percentage of defective panels is given as 6%. So, the equation can be written as:
0.10x + 0.03y = 0.06(x + y)
Now, let's solve for y.
First, simplify the equation:
0.10x + 0.03y = 0.06x + 0.06y
Rearrange the terms:
0.03y - 0.06y = 0.06x - 0.10x
Combine like terms:
-0.03y = -0.04x
Divide both sides by -0.03:
y = (0.04/0.03)x
Simplify further:
y = (4/3)x
Now, substitute the value of x using the fact that Plant A produced 9000 panels:
y = (4/3)(9000)
y = 12000
Therefore, Plant B produced 12000 panels.
A 9000 panels , 900 defective
B x panels, .03 x defective
panels = 9000 + x
defective panels = 900 + .03 x
.06 = (900+.03x)/(9000+x)