Question 1084820


The sum of the digits of a two digit number is 15. If 9 is added to the number the digits are interchange.

Suppose the digits are {{{x}}} and {{{y}}}, so the number is {{{10x + y}}}

if the sum of the digits of a two digit number is {{{15}}}, we have

{{{x+y=15}}}....solve for {{{x}}}
{{{x=15-y}}}..........eq.1

 If {{{9}}} is added to the number the digits are interchange:

 {{{10x + y+9=10y + x}}}

 {{{10x + y+9-10y - x=0}}}

 {{{9x -9y =-9}}}
 {{{x -y =-1}}}....solve for {{{x}}}

 {{{x  =y-1}}}.........eq.2

from eq.1 and eq2 we have

{{{15-y =y-1}}}

{{{15+1 =y+y}}}

{{{16 =2y}}}

{{{highlight(y=8)}}} ->  {{{x  =8-1}}}->{{{highlight(x=7)}}}

 so the number is {{{10x + y=10*7+8=highlight(78)}}}

check: If {{{9}}} is added to the number the digits are interchange:

{{{78+9=87}}} so, the digits are interchange