SOLUTION: Three times the tens digit of a certain two digit number is two more than four times the units digit. The difference between the given number and the number obtained by reversing t

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Question 402577: Three times the tens digit of a certain two digit number is two more than four times the units digit. The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number
Answer by mananth(16946) About Me  (Show Source):
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Three times the tens digit of a certain two digit number is two more than four times the units digit. The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number
...
let ten's digit be x
units digit be y
..
3x=4y+2
3x-4y=2...............1
...
10x+y-(10y+x)=2(x+y)-2
10x+y-10y-x=2x+2y-2
9x-9y=2x+2y-2
7x-11y=-2..............2
multiply (1) by 7 and (2) by -3
...
21x-28y=14
-21x+33y=6
add the two
5y=20
/5
y=4
..
plug y in (1)
3x-4y=2
3x-16=2
3x=18
/3
x=6
The number is 64