Percent mixture

Question

Two factory plants are making TV panels. Yesterday, Plant A produced twice as many panels as Plant B. Three percent of the panels from Part A and 5% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 990 defective panels?

Answer 1

Since Plant A produce twice as many panels as Plant B.

Let Plant B = x panels. 3% are defective or .03x

then

Plant A = 2x panels 5% are defective or .05(2x)= .10x

Together, Plant A and Plant B produce 990 panels

So, we have .10x+.03x=990

.13x=990

x=7615 panels

Answer 2

If a and b are the number of panels plants A and B produced, respectively, then a=2*b and also

990 = 0.03*a + 0.05*b. Replacing a=2b in this equation yields:

990 = 0.03*(2*b) + 0.05*b = 0.06*b + 0.05*b = 0.11*b ⇒ b=9000

and subsequently a= 2*b= 18000.