Half of a number added to its third part is eight less than the number. What is the number?

Expert Answers
justaguide eNotes educator| Certified Educator

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.

giorgiana1976 | Student

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.