## Elementary Algebra

Let the smaller number be $x$ and the larger number be $y$. Since the sum of the two numbers is 99, we obtain: $x+y=99$ Since the difference of the two numbers is 35, we obtain: $y-x=35$ Rearranging this equation to set the equation equal to $y$, we obtain: $y-x=35$ $y=35+x$ Therefore, we now have a pair of equations to solve. Substituting the second equation into the first equation, we obtain: $x+y=99$ $x+35+x=99$ $2x+35=99$ $2x=99-35$ $2x=64$ $x=32$ Substituting the value of $x$ in the first equation to find the value of $y$, we obtain: $x+y=99$ $32+y=99$ $y=99-32$ $y=67$ Therefore, the smaller number is 32 while the larger number is 67.