SOLUTION: THE SUM OF THE DIGITS OF A TWO-DIGIT NUMBER IS 12. IF THE DIGITS ARE REVERSED THE NEW NUMBER IS 18 LESS THAN THE ORIGINAL NUMBER. FIND THE ORIGINAL NUMBER.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: THE SUM OF THE DIGITS OF A TWO-DIGIT NUMBER IS 12. IF THE DIGITS ARE REVERSED THE NEW NUMBER IS 18 LESS THAN THE ORIGINAL NUMBER. FIND THE ORIGINAL NUMBER.      Log On


   

Question 185142: THE SUM OF THE DIGITS OF A TWO-DIGIT NUMBER IS 12.
IF THE DIGITS ARE REVERSED THE NEW NUMBER IS 18 LESS THAN THE ORIGINAL NUMBER.
FIND THE ORIGINAL NUMBER.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be N and the two digits be x and y
10%2Ax+%2B+y+=+N
y+=+N+-+10x
10%2Ay+%2B+x+=+N+-+18
10%2A%28N-10x%29+%2B+x+=+N+-18
10N+-+99x+=+N+-18
%289N+%2B18%29%2F99+=+x
x+%2B+y+=+12
x+%2B+N+-10x+=+12
-9x+=+12-N
-9%2A%289N%2B18%29%2F99+=+12+-+N
-9N+-+18+=+132+-+11N
2N+=+150
N+=+75
Check yor answer., is the sum of the digits 12? Is the difference between 75 and 57 equal to 18?