SOLUTION: In a two digit number one digit is even. Sum of original number and number obtained by interchanging digits is 11 times the difference between them. Find difference of digits in or

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Question 1104772: In a two digit number one digit is even. Sum of original number and number obtained by interchanging digits is 11 times the difference between them. Find difference of digits in original number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In a two digit number one digit is even.
Sum of original number and number obtained by interchanging digits is 11 times the difference between them.
Find difference of digits in original number.
:
Write the original number: 10a+b, where
a = the 1st digit
b = the 2nd digit
:
"Sum of original number and number obtained by interchanging digits is 11 times the difference between them."
(10a+b) + (10b+a) = 11((10b+a) - (10a+b))
Combine like terms
11a + 11b = 11(9b - 9a)
divide equation by 11
a + b = 9b - 9a
combine like terms
a + 9a = 9b - b
10a = 8b
5a = 4b
a = 4%2F5b
The only single integer solution: a=4; b=5; the number is 45
:
"Find difference of digits in original number. 1
:
:
Check solution in the statement
"Sum of original number and number obtained by interchanging digits is 11 times the difference between them."
45 + 54 = 11(54-45)
99 = 11(9)