Find the two-digit number satisfying the following two conditions: 1) Four times the units digit is six less than twice the tens digit. 2) The number is nine less than three times the number obtained by reversing the digits.
Accepted Solution
A:
-------------------------------------- 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. ----------------------------------------------------------------------------