Question 502890
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)