SOLUTION: A number of two digits is equal to 6 times the sum of the digits, and the number formed by reversing the digits exceeds 4 times the sum of the digits by 9. What is the original nu

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Question 989451: A number of two digits is equal to 6 times the sum of the digits, and the number formed by reversing the digits exceeds 4 times the sum of the digits by 9. What is the original number?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The original two digit number can be written as 10t + u where t = the tens digit and u = the ones digit
The first equation gives
10t + u = 6(t + u) [The number is 6 times the sum of the digits]
The second equation gives
10u + t = 4(t + u) + 9 [Reversing the digits equals the sum of the digits + 9]
We have two equations and two unknowns.
Solving for t in terms of u in the first equation gives t = (5/4)u
The 2nd equation gives t = 2u - 3
This gives u = 4, t = 5
Ans: 54
Check: 6*(5+4) = 54