Question

Two factory plants are making TV panels. Yesterday, Plant A produced 3 times as many panels as Plant B. Three percent of the panels from Plant A and 4% of the panels from Plant B were defective. How many panels did Plant A produce, if the two plants together produced 1300 defective panels?

Answer 1

Known equations:
A=3B
.03A +.04B = 1300

Substitute A=3B into second equation:
.03(3B) + .04B = 1300
.09B + .04B = 1300
.13B = 1300
B = 1300/.13 = 10,000 panels
A = 3(10,000) = 30,000 panels

**Plant A produced 30,000 panels

Double check:
.03(30,000) = 900
.04(10,000) = 400
900+400=1300 defective panels

Answer 2

Is there any other method besides the substitution method to do this? In class I don't think we did the substitution method.
Thank you soooo much though.

Answer 3

Substitution would be the easiest way, since you already have an equation where a one variable equals something (A=3B)
You could try doing it by elimination, but in my opinion that's much more tedious and harder to do since you're dealing with decimals.

Answer 4

Is there a way I can get rid of decimals? Like, wouldn't I multiply everything by 100 in order to make it a whole number?

Answer 5

Elimination:
A-3B = 0
.03A + .04B = 1300
Multiply second equation by 100:
A-3B = 0
3A +4B = 130000
Easiest way is to multiply top equation by -3
-3A+9B = 0
3A+4B = 130000
Add:
13B = 130000
B = 10,000
Then just do the same steps above to find A again.

Answer 6

Ok, that helps a lot. Thank you so much c: