SOLUTION: One number is 12 less than another. If 10 times the smaller number minus 2 times the larger number is 8, find the two numbers

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Question 118026: One number is 12 less than another. If 10 times the smaller number minus 2 times the larger number is 8, find the two numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=one number (smaller number) and y=another number (larger number)
The sentence "One number is 12 less than another" translates to x=y-12 and the sentence "10 times the smaller number minus 2 times the larger number is 8" translates to 10x-2y=8

So we get the system

x=y-12
10x-2y=8


Start with the given system
10x-2y=8
x=y-12



10%28y-12%29-2y=8 Plug in x=y-12 into the first equation. In other words, replace each x with y-12. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


10y-120-2y=8 Distribute


8y-120=8 Combine like terms on the left side


8y=8%2B120Add 120 to both sides


8y=128 Combine like terms on the right side


y=%28128%29%2F%288%29 Divide both sides by 8 to isolate y



y=16 Divide




Now that we know that y=16, we can plug this into x=y-12 to find x



x=%2816%29-12 Substitute 16 for each y


x=4 Simplify


So our answer is x=4 and y=16 which means our numbers are 4 and 16