Question 1085222


you are told:


A number consists of two digits sum of its digit is 15.


if the place of digits are interchanged, then the number obtained is 9 less than the original number.


and you are asked:


find the original number


let ab be the original number.


the value of ab is 10 * a + b.


if the original number is ab, then the number with the digits interchanged would be ba.


the value of the number would then be 10 * b + a.


you are told that the sum of the digits is 15 and, if the place of the digits are interchanged, then the number obtained is 9 less than the original number.


this gets you a + b = 15 and 10b + a = 10a + b - 9


you have 2 equations that need to be solved simultaneously.


they are:


a + b = 15


10b + a = 10a + b - 9



in the first equation, solve for b to get b = 15 - a


in the second equation, replace b with 15 - a to get:


10 * (15 - a) + a = 10a + (15 - a) - 9


simplify to get:


150 - 10a + a = 10a + 15 - a - 9


combine like terms to get:


150 - 9a = 9a + 6


subtract 6 from both sides of the equation and add 9a to both sides of the equation to get 144 = 18a.


divide both sides of the equation by 18 to get 144/18 = a


solve for a to get a = 144/18 = 8


since a + b = 15, then b must be equal to 7.


the original number is ab which is 87.


the new number is ba which is equal to 78 which is equal to 9 less than 87.


the sum of the digits is 15.


all the requirements of the problem have been satisfied, so the solution looks good.