Question 45976
<pre><font color=blue>One number</font> is 12 more than <font color=green>another</font>.  The sum of the <font color=green>smaller number</font> and twice the <br><font color=blue>larger number</font> is 39.  Find the larger number.

Let us assign <font color=green>x</font> to the <i>smaller number</i> and <font color=blue>y</font> to the <i>larger number</i>.

From the first sentence we derive the following equation:
<font color=blue>X</font>=<font color=green>Y</font>+12
From the second, we derive the following:
<font color=green>Y</font>+2<font color=blue>X</font>=39

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

Since we know <font color=green>Y</font> is equal to 5, we can replace it into the equation <font color=blue>X</font>=<font color=green>Y</font>+12.  <br>This yields:
<font color=blue>X</font>=5+12, or 17.

<font color=blue>X</font>=17
<font color=green>Y</font>=5</pre>