The sum of the digits of a two-digit number is 6. When the digits are reversed, the resulting number is 6 greater than 3 times the original number. Find the original number
The number is = 15
The two digits are = 1 + 5 = 6
Reverse 15 and you get 51
3 x 15 + 6 = 51
A more algebraic way would be:\(3(10x+y)+6=10y+x\) . Now, we have \(30x+3y+6=10y+x\) . Solving, we get \(29x+6=7y. \) Solve it, and you should get 15.
+130031 Let the digits be x and y
Let the original number = 10x + y
So
x + y = 6 ⇒ y = 6 - x (1)
And we know that
3 (10x + y) + 6 = (10y + x)
30x + 3y + 6 = 10y + x (2) sub (1) into (2)
30x + 3( 6 - x) + 6 = 10(6 - x) + x
30x + 18 - 3x + 6 = 60 - 10x + x
27x + 24 = 60 - 9x
36x = 36
x = 1
And y = 6 - x = 6 - 1 = 5
The original number is
10x + y = 10(1) + 5 = 15
