SOLUTION: In a two digit number , the digit at unit's place is equal to the square of the digit at tens place . If 54 is added to the number , the digit gets interchanged . Find the number.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: In a two digit number , the digit at unit's place is equal to the square of the digit at tens place . If 54 is added to the number , the digit gets interchanged . Find the number.      Log On


   

Question 695143: In a two digit number , the digit at unit's place is equal to the square of the digit at tens place . If 54 is added to the number , the digit gets interchanged . Find the number.
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
First you need to know how you can write a number of two digits:
23=2*10+3
Following the example above, now my number is xy
xy=x*10+y
and the reverse digits number is yx
yx=y*10+x
What we know is:
y=x%5E2
and
10x%2By%2B54=10y%2Bx
Bring everything to the right side in the second equation:
0=9y-9x-54
Divide entire equation by 9:
0=y-x-6
Replace y with x%5E2
0=x%5E2-x-6
0=%28x-3%29%28x%2B2%29
So x is either 3 or -2. The second choice cannot be as a digit in a number cannot be negative. So x=3 and y=9. Thus the number is 39.