Question

Two factory plants are making TV panels. Yesterday, Plant A produced 3000 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 1070 defective panels?

Answer 1

The first step is to choose two variables to represent the numbers of panels made in each plant.

Answer 2

A= b-3000

Answer 3

Good.
You already have the two variables and the first equation.

Answer 4

Now we need a second equation.

Answer 5

How do you write 4% of A?

Answer 6

A.04

Answer 7

0.04A

Answer 8

a*.04

Answer 9

oh okay

Answer 10

Now do the same for 3% of B

Answer 11

B.03

Answer 12

0.03B is better.

Answer 13

yes

Answer 14

The numbers of defective panels are 0.04A and 0.03B, right?

Answer 15

yes

Answer 16

Now add them together and set the sum equal to 1070.
That's the second equation.

Answer 17

.07=1070

Answer 18

No.
0.04A and 0.03B are unlike terms. They can't be combined together.
Their sum must be written as 0.04A + 0.03B

Answer 19

The second equation is:
0.04A + 0.03B = 1070

Answer 20

correct

Answer 21

Now you have two equations:
A = B - 3000
0.04A + 0.03B = 1070
Now you need to solve the system of equations.

Answer 22

Since the first equation is already solved for A, we can use substitution easily.

Answer 23

Replace A of the second equation with B - 3000.
Then you will have an equation with only B, and you can solve it for B.

Answer 24

.04A(b-3000)+.03=1070

Answer 25

no

Answer 26

.04(b-3000)+.03=1070

Answer 27

There is still a B with 0.03

Answer 28

yes so 7b-120=1070?

Answer 29

b=170

Answer 30

.07

Answer 31

\(\color{red}{A = B - 3000}\)
\(0.04\color{red}{A} + 0.03B = 1070\)
\(0.04\color{red}{(B - 3000)} + 0.03B = 1070\)

Answer 32

17000

Answer 33

b=17000?

Answer 34

0.04B - 120 + 0.03B = 1070
0.07B - 120 = 1070
0.07B = 1190
B = 17,000

Answer 35

a= 14000?

Answer 36

Correct.
A = B - 3000
A = 17,000 - 3000
A = 14,000

Answer 37

You are correct.

Answer 38

YAY

Answer 39

Answer:
Plant A produced 14,000 panels.

Answer 40

Thank you

Answer 41

You're welcome.