SOLUTION: A two digit number is three less than seven times the sum of its digits, if the digits are reversed, the number is 18 less than the original number. what is the original number.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A two digit number is three less than seven times the sum of its digits, if the digits are reversed, the number is 18 less than the original number. what is the original number.       Log On


   

Question 501666: A two digit number is three less than seven times the sum of its digits, if the digits are reversed, the number is 18 less than the original number. what is the original number.


Answer by geetha_rama(94) About Me  (Show Source):
You can put this solution on YOUR website!
Let XY be the two dight number.
Expanding this number we have,
10X + Y = 7(X+Y) -3
10X + Y -7X -7Y = -3
3X -6Y = -3
X -2Y = -1 -> Equation 1
Now the reversed number will be YX
10Y + X = 10X + Y -18
10Y -Y +X -10X = -18
9Y - 9X = -18
Y -X = -2 _> Equation 2
From equation 1, 2
X -2y = -1
-X + Y = -2
=> -Y = -3
Y = 3
X -2Y = -1
X = 2Y - 1 = 6 -1 = 5
Original Number = 53
Check:
Reversed number is 18 less than original number
35 + 18 = 53