SOLUTION: In a number of two digits, the sum of the digit is 6. if the digits change their places, hte new number so formed is three times the digits in the tens place of the original number

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Question 188627: In a number of two digits, the sum of the digit is 6. if the digits change their places, hte new number so formed is three times the digits in the tens place of the original number.Find the number
Answer by Mathtut(3670) About Me  (Show Source):
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In a number of two digits, the sum of the digit is 6. if the digits change their places, hte new number so formed is three times the digits in the tens place of the original number.Find the number
:
let the number be ab...which can be written as 10a+b
if digits are changed we have ba which can be written as 10b+a
:
a+b=6...............eq 1
10b+a=3a............eq 2
:
rewrite eq 1 to a=6-b and plug this into eq 2 for every occurrence of a
:
10b+6-b=3(6-b)
:
9b+6=18-3b
:
12b=12
:
b=1
:
a=6-1=5
:
orginal # is 51