SOLUTION: A number consist of two digit whose sum is 9.If the place of the digit are interchanged then the new number is 5/6 times the original number .the number is

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Question 905430: A number consist of two digit whose sum is 9.If the place of the digit are interchanged then the new number is 5/6 times the original number .the number is
Answer by Fombitz(32388) About Me  (Show Source):
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A%2BB=9
The original number is 10A+B
The interchanged number is 10B+A.
10B%2BA=%285%2F6%29%2810A%2BB%29
6%2810B%2BA%29=5%2810A%2BB%29
60B%2B6A=50A%2B5B
55B-44A=0
5B-4A=0
Multiply the first equation by 5 and add to this equation,
4A%2B4B%2B5B-4A=36%2B0
9B=36
B=4
Then,
A%2B4=9
A=5
The original number is 54, the interchanged number is 45.