Question 237192
Since we know one number is one third of another number, we can say:
x = one number
1/3x = the other number
Now, we also know their sum equals the larger # minus 1, so here's your equation:
{{{x+(1/3)x=x-1}}}
Now solve for x to find the first number:
{{{(1/3)x=x-1-x}}}
{{{(1/3)x=-1}}} ...multiply by 3 on both sides...
{{{x=-3}}}  This is your first number.
Now calculate your second number by pluging this value in 
{{{(1/3)x}}}
{{{(1/3)-3}}}
{{{-1}}}  This is your second number.
.
Proof:
Plug in these values in the original equation.  Both sides of the eqn must equal to each other.
{{{x+(1/3)x=x-1}}} ...by substitution...
{{{-3+(-1)=(-3)-1}}}
{{{-4=-4}}}
Done!