SOLUTION: pls. help me solve this problem... thank you... problem 1. Three times the tens digit of a certain two digit number is two more than four times the units digit. The difference

Question 351512: pls. help me solve this problem... thank you...
problem 1. 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.
problem 2. Find the two digit number such that four times the units digit is six less than twice the tens digit, and the number is nine less than the three times the number obtained by reversing the digits.

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
problem 1. 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 10's digit be x & unit's digit be y
3x=2+4y
3x-4y=2................1
10x+y -(10y+x)=2(x+y)-2
10x+y-10y-x=2x+2y-2
10x-x-2x-10y+y-2y=-2
7x-11y=-2...............2
multiply equation 1 by -7 and 2 by 3 and add the equations
..
-21x+28y=-14
21x-33y=-6
-5y=-20
y=4
plug the value of 4 in the equation 1
3x-4*4 = 2
3x-16=2
3x=18
x=6
the number is 64
...
problem 2. Find the two digit number such that four times the units digit is six less than twice the tens digit, and the number is nine less than the three times the number obtained by reversing the digits.
let 10's digit be x & unit's digit be y
4y=2x-6
4y-2x=-6
/2
2y-x=-3.................1
10x+y = 3(10y+x)-9
10x+y -30y-3x=-9
7x-29y=-9...............2
multiply eq 1 by 7 add it to eq. 2
14y-7x-21
add
-15y=-30
y=2
plug value of y in equation 1
2y-x=-3
4-x=-3
x=4+3
x=7
....
m.ananth@hotmail.ca
The number = 74

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