Answer
17, 85
Work Step by Step
Let the smaller number be $x$ and the larger number be $y$.
Since the sum of the two numbers is 102, we know:
$x+y=102$
Since if the larger number is subtracted from 6 times
the smaller number, the result is equal to the smaller number, we know:
we write
$6x-y=x$
$6x-x=y$
$5x=y$
$y=5x$
Therefore, we now have a pair of equations to solve. Substituting the second equation into the first equation, we obtain:
$x+y=102$
$x+5x=102$
$6x=102$
$x=17$
Substituting the value of $x$ in the first equation to find the value of $y$, we obtain:
$x+y=102$
$17+y=102$
$y=102-17$
$y=85$
Therefore, the smaller number is 17 while the larger number is 85.
