--------------------------------------
Define x :
--------------------------------------
Let the two digit number be 10x + y.
--------------------------------------
Construct Equation :
--------------------------------------
Four times the units digit is six less than twice the tens digit
⇒ 4y = 2x - 6
⇒2y = x - 3
⇒ x = 2y + 3
The number is nine less than three times the number obtained by reversing the digits.
⇒10x + y = 3(10y + x) - 9
⇒ 10x + y = 30y + 3x - 9
⇒ 7x = 29y - 9
--------------------------------------
Solve for x and y :
--------------------------------------
x = 2y + 3 ----------------------- (1)
10x = 29y - 9 ------------------- (2)
Sub (1) into (2) :
7(2y + 3) = 29y - 9
14y + 21 = 29y - 9
15y = 30
y = 2 ------------------- Sub into (1)
x = 2(2) + 3
x = 7
--------------------------------------
Find the number:
--------------------------------------
Number = 10x + y = 10(2) + 7 = 27
----------------------------------------------------------------------------
Answer: The 2-digit number is 27.
----------------------------------------------------------------------------
