SOLUTION: The quotient of a two-digit number divided by the sum of its digit is 4. If the number is subtracted from the sum of the squares of its digits, the difference is 9. Find the number

Algebra ->  Test -> SOLUTION: The quotient of a two-digit number divided by the sum of its digit is 4. If the number is subtracted from the sum of the squares of its digits, the difference is 9. Find the number      Log On


   

Question 1186765: The quotient of a two-digit number divided by the sum of its digit is 4. If the number is subtracted from the sum of the squares of its digits, the difference is 9. Find the number.
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
The quotient of a two-digit number divided by the sum of its digit is 4.
%2810t%2Bu%29%2F%28t%2Bu%29=4
If the number is subtracted from the sum of the squares of its digits, the difference is 9.
t%5E2%2Bu%5E2-%2810t%2Bu%29=9
Find the number.

system%28%2810t%2Bu%29%2F%28t%2Bu%29=4%2Ct%5E2%2Bu%5E2-%2810t%2Bu%29=9%29

system%2810t%2Bu=4%28t%2Bu%29%2Ct%5E2%2Bu%5E2-10t-u=9%29

system%2810t%2Bu=4t%2B4u%2Ct%5E2%2Bu%5E2-10t-u=9%29

system%286t=3u%2Ct%5E2%2Bu%5E2-10t-u=9%29

system%282t=u%2Ct%5E2%2Bu%5E2-10t-u=9%29

t%5E2%2B%282t%29%5E2-10t-%282t%29=9

t%5E2%2B4t%5E2-10t-2t=9

5t%5E2-12t=9

5t%5E2-12t-9=0

%285t%2B3%29%28t-3%29=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