SOLUTION: Three times the ten's digit of a certain two-digit number is two more than 4 times the unit's digit. The difference of the original number and the number obtained by reversing the

Algebra ->  Matrices-and-determiminant -> SOLUTION: Three times the ten's digit of a certain two-digit number is two more than 4 times the unit's digit. The difference of the original number and the number obtained by reversing the       Log On


   

Question 265441: Three times the ten's digit of a certain two-digit number is two more than 4 times the unit's digit. The difference of the original number and the number obtained by reversing the digit is two less than twice the sum of the digits. Find the original number.
Answer by vksarvepalli(154) About Me  (Show Source):
You can put this solution on YOUR website!
let the two digit number be xy (x- tens digit & y- units digit)
so number value=10x+y
reversed digit is yx and its value is 10y+x
given 3x = 2+4y --------------1 (so x>y and also xy>yx)
and also given that
(10x+y)-(10y+x) = 2(x+y)-2
=> 9x-9y = 2x+2y-2
=> 7x = 11y-2 ----------------2
multiply equation-1 by 7 and equation-2 by 3 and then subtract
we get 14+28y = 33y-6
=> 5y=20
=> y=4
and 3x=2+16=18
so x=6
so the two digit number is 64