SOLUTION: Please help us write out this equation. I couldn't find anything like this problem in your previous answers. This problem is word for word from my son's algebra book. The sum of

Question 28142: Please help us write out this equation. I couldn't find anything like this problem in your previous answers. This problem is word for word from my son's algebra book.
The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 less than the original. Find the original number.
Thanks a billion in advance for your help.
Found 2 solutions by longjonsilver, sdmmadam@yahoo.com:
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
Let the number be written as xy, where x is the number of tens and y in the number of units.

x+y = 9 --eqn1

original number is (10x + y)
reversed number is (10y + x)

reversed = original - 27
(10y + x) = (10x + y) - 27
10y + x = 10x + y - 27
9y - 9x = -27
or -9y + 9x = 27 ... just reversing all signs (equivalent to moving all terms to opposite side of equals sign)

so -9y + 9x = 27 is
9x - 9y = 27 --eqn2

so we have 2 equations and 2 unknowns...possible to solve.
x + y = 9 -- multiply by 9
9x - 9y = 27

9x + 9y = 81
9x - 9y = 27
and add together giving 18x = 108
--> x = 6
therefore y must be 3

so numbers are 63 and 36 and their difference is 27...correct.

jon.

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 less than the original. Find the original number.
Let the digit in the units place be u and
let the digit in the tens place be t
Then the two digit number is givn by (10t+u)----(*)
By data the sum of the digits of the two digit number is 9
That is (u+t) = 9----(1)
Now if the digits are reversed, that is u and t switch places then now t is the unit place digit and u is the tenth place digit
This reversed number is (10u+t)and it is given to be 27
That is (10u+t) = 27 ----(2)
Putting (1) in (2) (using t = 9-u )
10u +(9-u) = 27
(10u-u)= 27-9
9u = 18
u = 18/9 = 2
u= 2 in (1): u+t = 9 implies t = 7
Therefore the original number is got by putting t=7 and u =2 in (*)
(10t+u) = 10X7 + 2 = 70+2 = 72
Answer: The required number is 72
Verification: IF we add up the digits in 72 we get 9 and 72 when reversed is 27.
Therefore our answer72 is correct
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