Answer to Question #31934 in Algebra for vishnupriya

Question

The sum of two digits of a two-digit number is 13. If the digits are interchanged, and the resulting number is added to the original number, then we get 143. What is the original number?

Answer 1

Let x and y are digits of the number z. Then x+y=13.Hence, the number can be written as z=xy
But it means that z=10*x+y. If we interchange digits we'llget yx=10*y+x
xy+yx=11*x+11*y=11(x+y)
We know that 11(x+y)=143, therefore x+y=13
We obtain the same equation so for every pair x, y - digitssuch that x+y=13 we get that we need x=4, y=9 x=5, y=8 x=6, y=7 x=7, y=6 x=8,
y=5 x=9, y=4
All such numbers are 49, 58, 67, 76, 85, 94