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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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