SOLUTION: A two digit number is 3 times the sum of it's digits. The number is also 45 less than the number formed by reversing the digits and the original number. What is the original number

Question 502890: A two digit number is 3 times the sum of it's digits. The number is also 45 less than the number formed by reversing the digits and the original number. What is the original number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = the 10's digit, let y = the units
:
A two digit number is 3 times the sum of it's digits.
10x + y = 3(x+y)
10x + y = 3x + 3y
10x - 3x = 3y - y
7x = 2y
:
The number is also 45 less than the number formed by reversing the digits and the original number.
10x + y = 10y - x - 45
10x - x = 10y - y - 45
9x = 9y - 45
simplify, divide by 9
x = y - 5
:
In the 1st simplified equation replace x with (y-5)
7(y-5) = 2y
7y - 35 = 2y
7y - 2y = 35
5y = 35
y = 35/5
y = 7 is the units digit (original number)
and
x = 7 - 5
x = 2 is the 10's digit
:
27 is the number
:
:
Check it in the statement:
"A two digit number is 3 times the sum of it's digits.
27 = 3(7+2)
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