-------------------------------------- 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. ----------------------------------------------------------------------------
