## Elementary Algebra

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.