Answer
36,42
Work Step by Step
Let the smaller number be $x$ and the larger number be $y$.
Since the sum of the two numbers is 78, we obtain:
$x+y=78$
Since the smaller number subtracted from the larger number produces 6, we know:
$y-x=6$
$y=6+x$
Therefore, we now have a pair of equations. Substituting the second equation into the first equation, we obtain:
$x+y=78$
$x+(6+x)=78$
$2x+6=78$
$2x=78-6$
$2x=72$
$x=36$
Substituting the value of $x$ in the first equation to find the value of $y$, we obtain:
$x+y=78$
$36+y=78$
$y=78-36$
$y=42$
Therefore, the smaller number is 36 while the larger number is 42.
