Question 901220
x and y. They are INTEGERS.
{{{x+y=23}}}, and {{{xy>76}}}.


{{{y=23-x}}}; substitute into the inequality.
{{{x(23-x)>76}}}
{{{-x^2+23x>76}}}
{{{-x^2+23x-76>0}}}
{{{highlight_green(x^2-23x+76<0)}}}


{{{(x-19)(x-4)<0}}}


You want integers between 4 and 19.  You do not want these two values included,
because the problem specified a strict inequality, product GREATER than 76.
5 & 18 ? Yes.
6 & 17 ? Yes.
.
.
11&12?  Yes.


ANSWER:  Lowest number 5; highest number 18,
whose sum is 23.