Question

If three times a number, added to 4 is divided by the number plus 7, the result is five halves. How do you find the number?

Answer 1

`(4 + 3n)/(n + 7) = 5/2` solved is `n = 27`

Explanation:

First, let the number we are looking for be represented by `n`.

"three times a number" can then be written as `3n`.

`3n` "added to 4" can this be written as `4 + 3n`

"the number plus 7" can be written as `n + 7`

`4 + 3n` "is divided by" `n + 7` can be written as `(4 + 3n)/(n + 7)`

"the result is" is `=`

And "five halves" is `5/2`

So, combining this all together gives:

`(4 + 3n)/(n + 7) = 5/2`

Then solving this for `n` while keeping the equation balanced gives:

`(n + 7)(4 + 3n)/(n + 7) = 5/2(n + 7)`

`4 + 3n = (5n)/2 + 35/2`

`8/2 + (6n)/2 = (5n)/2 + 35/2`

`8/2 + (6n)/2 - 8/2 - (5n)/2 = (5n)/2 + 35/2 - 8/2 - (5n)/2`

`n/2= 27/2`

`(2n)/2 = 2 * 27/2`

`n = 27`