SOLUTION: the sum of the digits of a two digit number is 8. if 8 is subtracted from the number the digits interchange their places.find the number.

Question 834553: the sum of the digits of a two digit number is 8. if 8 is subtracted from the number the digits interchange their places.find the number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let a = the 10's digit
Let b = the units
then
10a+b = "the number"
:
There is no integer solutions from the way this is written,
Change 8 to 9 and it works
:
the sum of the digits of a two digit number is 9.
a + b = 9
a = (9-b); use this form for substitution
:
if 9 is subtracted from the number, the digits interchange their places.
10a + b - 9 = 10b + a
10a - a = 10b - b + 9
9a = 9b + 9
simplify, divide by 9
a = b + 1
replace a with (9-b)
9 - b = b + 1
9 - 1 = b + b
8 = 2b
b = 4
then
a = 5
find the number. 54
:
:
Check
54 - 9 = 45
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