Answer
32,67
Work Step by Step
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.
