SOLUTION: if a company plans to lay off 10% of its employees in its aerospace division and 15% of its employees in its agricultural divsion. If altogether 12% of the 3000 employees in these

Question 162853: if a company plans to lay off 10% of its employees in its aerospace division and 15% of its employees in its agricultural divsion. If altogether 12% of the 3000 employees in these two division will be laid off, then how many employees are in each divsion.
Heres what I've tried: .10 (x) + .15(x) +.12 = 3000
300 450
.12x = 3000
____ ____
.12 .12
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of aerospace employees and y=# of agricultural employees

From the problem, we know that there are a total of 3,000 employees from both divisions. So this means that the sum of the two groups will be 3,000. This means that

Also, since 12% of the total workers will be laid off, this means that 0.12(3000)=360 employees will be laid of in total in these two divisions. So the sum of the layoffs in the aerospace division (which is 10% of "x" and is represented by 0.10x) and the layoffs in the aerospace division (which is 15% of "y" and is represented by 0.15y) will equal 360. This translates to: )

Start with the second equation

Multiply EVERY term by 100 to make every number a whole number. Note: this will move the decimal point two spots to the right.

So we have the system of equations:

Multiply the both sides of the first equation by -10.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms. Notice how the x terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

This means that there are 1,800 aerospace employees and 1,200 agricultural employees (before the layoffs).

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