One number is 12 more than another.  The sum of the smaller number and twice the 
larger number is 39.  Find the larger number.

Let us assign x to the smaller number and y to the larger number.

From the first sentence we derive the following equation:
X=Y+12
From the second, we derive the following:
Y+2X=39

We know X is equal to Y+12, so we'll replace the X in the second equation with (Y+12).
The second equation now yields:
Y+2(Y+12)=39.  Let us simplify by distribution:
Y+2Y+24=39  Simplify and minus 24 on both sides:
3Y=15  Divide both sides by 5:
Y=5  We found Y!

Since we know Y is equal to 5, we can replace it into the equation X=Y+12.  
This yields:
X=5+12, or 17.

X=17
Y=5