Question 799190
<br>One number is 6 more than the other, and their sum is 44.  Suppose we subtract 6 from the larger number; now both the numbers are the same, and their sum is 38.  That would make the two numbers each equal to 19.  But in fact the numbers are not the same; one is 6 larger than the other.  So add 6 to one of the 19s and you get the two numbers: 19 and 25.
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That's the informal solution.  Algebraically what I did was this:<br>
{{{x+(x+6)=44}}}
{{{2x+6=44}}}
{{{2x=38}}}
{{{x=19}}}
{{{x+6=25}}}
<br>Especially when you are first learning algebra, it is nice to see that the formal algebra does exactly what you might do informally to solve the problem....