Question 1186765
The quotient of a two-digit number divided by the sum of its digit is 4.

{{{(10t+u)/(t+u)=4}}}

If the number is subtracted from the sum of the squares of its digits, the difference is 9. 

{{{t^2+u^2-(10t+u)=9}}}

Find the number.<pre>

{{{system((10t+u)/(t+u)=4,t^2+u^2-(10t+u)=9)}}}

{{{system(10t+u=4(t+u),t^2+u^2-10t-u=9)}}}

{{{system(10t+u=4t+4u,t^2+u^2-10t-u=9)}}}

{{{system(6t=3u,t^2+u^2-10t-u=9)}}}

{{{system(2t=u,t^2+u^2-10t-u=9)}}}

{{{t^2+(2t)^2-10t-(2t)=9}}}

{{{t^2+4t^2-10t-2t=9}}}

{{{5t^2-12t=9}}}

{{{5t^2-12t-9=0}}}

{{{(5t+3)(t-3)=0}}}

5t+3=0;   t-3=0
  5t=-3;    t=3
   t=-3/5;  

Only t=3 can be a digit, so ignore -3/5

Substitute in

  2t=u
2(3)=u
   6=u

So the tens digit is 3 and the units digit is 6,

so the answer is 36.

Edwin</pre>