SOLUTION: The value of a certain two digit number is 2 times the sum of it's digits. If the digits are reversed, the resulting number is 4.5 times the original number. What is the original n

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Question 551133: The value of a certain two digit number is 2 times the sum of it's digits. If the digits are reversed, the resulting number is 4.5 times the original number. What is the original number? Please help me solve this!!
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The value of a certain two digit number is 2 times the sum of it's digits. If the digits are reversed, the resulting number is 4.5 times the original number. What is the original number?
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t = 10s digit
u = 1s digit
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10t + u = 2*(t+u)
10u + t = 4.5*(10t + u)
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Can you finish it?
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PS it's = it is

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The value of a certain two digit number is 2 times the sum of it's digits.
If the digits are reversed, the resulting number is 4.5 times the original number.
:
Let a = the 10's digit
Let b = the units digit
then 10a + b = the original number
:
"the value of a two digit number is 2 times the sum of it's digits."
10a + b = 2(a + b)
10a + b = 2a + 2b
10a - 2a = 2b - b
8a = b
Pretty obvious, the only value that a can be is 1, to give a single digit value for b
18 is the original number
:
"If the digits are reversed, the resulting number is 4.5 times the original number."
81 = 4.5(18)
81 = 81