SOLUTION: The difference between the digits of a two-digit number is 1. The number itself is 1 more than 5 times the sum of its digits. If the units digit is greater than the tens digit, fin

Algebra ->  Equations -> SOLUTION: The difference between the digits of a two-digit number is 1. The number itself is 1 more than 5 times the sum of its digits. If the units digit is greater than the tens digit, fin      Log On


   

Question 1179664: The difference between the digits of a two-digit number is 1. The number itself is 1 more than 5 times the sum of its digits. If the units digit is greater than the tens digit, find the number.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x units
y ten's
value of number 10y+x
The difference between the digits of a two-digit number is 1.
y-x=1 -----------------(1)
The number itself is 1 more than 5 times the sum of its digits. If the units digit is greater than the tens digit, find the number.
10x+y =5(x+y)+1
10x+y = 5x+5y+1
5x-4y=1--------------------(2)
x ten's digit
y units digit


-1 x + 1 y = 1


5 x + -4 y = 1 .............2
Eliminate y
multiply (1)by 4
Multiply (2) by 1
-4 x 4 y = 4
5 x -4 y = 1
Add the two equations
1 x = 5
/ 1
x = 5
plug value of x in (1)
-1 x + 1 y = 1
-5 + 1 y = 1
1 y = 6
y = 6
Ans x = 5
y = 6
5 ten's digit
6 units digit