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

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) (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 and the sentence "10 times the smaller number minus 2 times the larger number is 8" translates to

So we get the system

Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Add 120 to both sides

Combine like terms on the right side

Divide both sides by 8 to isolate y

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and which means our numbers are 4 and 16

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