Let the number we need to find be N.
As half of the number added to its third part is eight less than the number, we get
N/2 + N/3 = N - 8
=> (3N + 2N)/6 = (N - 8)
=> 5N = 6N - 48
=> N = 48
The required number is 48.
Let x to be the unknown number.
In algebra, the verbal expression "half of the number" = x/2.
In the same way, the verbal expression "the 3rd part" = x/3
We'll create the left side of the equation:
Half of a number added to its third part is: x/2 + x/3 =
In algebra, "is" means "="
We'll create the right side of equation:
"eight less than the number" x - 8
The equation is:
x/2 + x/3 = x - 8
We'll multiply by 6 the equation:
3x + 2x = 6x - 48
5x - 6x = -48
-x = -48
x = 48
The unknown number is x = 48.