<PRE><B>Question 1119269</B>
a number consists of 2 digits whose sum is 9.
if 9 is subtracted from the number, the digits interchange.
find the number.


let a = the first digits and let b equal the second digit.


the value of the number is 10a + b.


the sum of the digits is 9, therefore a + b = 9.


if you substract 9 from the number, then the digits interchange, therefore:


10a + b - 9 = 10b + a


subtract a from both sides of this equation and subtract b from both sides of this equation to get:


9a - 9 = 9b


since a + b = 9, solve for a to get a = 9 - b.


in the equation of 9a - 9 = 9b, replace a with 9 - b to get:


9 * (9 - b) - 9 = 9b


simplify to get:


81 - 9b - 9 = 9b


add 9b to both sides of the equaiton and combine like terms to get:


72 = 18b.


solve for b to get b = 72/18 = 4.


since a + b = 9, then a must be 5.


you have a = 5 and b = 4.


the number is 54.


subtract 9 from it and the number becomes 45.


your solution is that the number is equal to 54.







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