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

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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(21684) About Me  (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 x%2By=3000


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: 0.10x%2B0.12y=360)


0.10x%2B0.15y=360 Start with the second equation


10x%2B15y=36000 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:

system%28x%2By=3000%2C10x%2B15y=36000%29


-10%28x%2By%29=-10%283000%29 Multiply the both sides of the first equation by -10.


-10x-10y=-30000 Distribute and multiply.


So we have the new system of equations:

system%28-10x-10y=-30000%2C10x%2B15y=36000%29


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


%28-10x-10y%29%2B%2810x%2B15y%29=%28-30000%29%2B%2836000%29


%28-10x%2B10x%29%2B%28-10y%2B15y%29=-30000%2B36000 Group like terms.


0x%2B5y=6000 Combine like terms. Notice how the x terms cancel out.


5y=6000 Simplify.


y=%286000%29%2F%285%29 Divide both sides by 5 to isolate y.


y=1200 Reduce.


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-10x-10y=-30000 Now go back to the first equation.


-10x-10%281200%29=-30000 Plug in y=1200.


-10x-12000=-30000 Multiply.


-10x=-30000%2B12000 Add 12000 to both sides.


-10x=-18000 Combine like terms on the right side.


x=%28-18000%29%2F%28-10%29 Divide both sides by -10 to isolate x.


x=1800 Reduce.


So our answer is x=1800 and y=1200.


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