Question

If one-half of a number is 8 less than two-thirds of the number, what is the number?

Answer 1

The number is `48`

Explanation:

First, let's call the number we are looking for `n`.

We can then write "two-thirds of the number" as `2/3 n`

We can also write "one-half of a number" as `1/2 n`

Finally we are told

`1/2 n` is the same as `2/3 n - 8` or:

`1/2 n = 2/3 n - 8`

We can now solve for `n`:

`1/2n - 2/3n = 2/3n - 8 - 2/3n`

`1/2n - 2/3n = -8`

We next need to get the fractions over common denominators, in this case `6` by multiplying each fraction by the necessary for of `1`:

`(3/3) 1/2n - (2/2) 2/3n = -8`

`3/6n - 4/6n = -8`

`-1/6 n = -8`

We can finally solve for `n` by multiplying by -6 to isolate `n`

`-6 * (-1/6)n = -8 * -6`

`1n = 48`

`n = 48`