SOLUTION: five times the sum of the digits of a two digit number equals the number. if the digits are reversed, it becomes nine more than the original number. what is the original number?

Question 564765: five times the sum of the digits of a two digit number equals the number. if the digits are reversed, it becomes nine more than the original number. what is the original number?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
five times the sum of the digits of a two digit number equals the number. if the digits are reversed, it becomes nine more than the original number. what is the original number?
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Let the original number be 10t + u
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Equation:
5(t+u) = 10t+u
10u+t = 10t+u + 9
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Modify:
5t-4u = 0
9t-9u = -9
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Modify:
5t-4u = 0
t = u-1
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Substitute for "t" and solve for "u":
5(u-1)-4u = 0
u = 5
---
Solve for "t":
t = u-1
t = 4
===============
Original number: 45
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Cheers,
Stan H.
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