2001 AMC 8 Problems/Problem 2
Let the numbers be and
. Then we have
and
. Solving for
in the first equation yields
, and substituting this into the second equation gives
. Simplifying this gives
, or
. This factors as
, so
or
, and the corresponding
values are
and
. These are essentially the same answer: one number is
and one number is
, so the largest number is
.