# 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?

Nov 9, 2016

$\frac{4 + 3 n}{n + 7} = \frac{5}{2}$ 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 $3 n$.

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

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

$4 + 3 n$ "is divided by" $n + 7$ can be written as $\frac{4 + 3 n}{n + 7}$

"the result is" is $=$

And "five halves" is $\frac{5}{2}$

So, combining this all together gives:

$\frac{4 + 3 n}{n + 7} = \frac{5}{2}$

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

$\left(n + 7\right) \frac{4 + 3 n}{n + 7} = \frac{5}{2} \left(n + 7\right)$

$4 + 3 n = \frac{5 n}{2} + \frac{35}{2}$

$\frac{8}{2} + \frac{6 n}{2} = \frac{5 n}{2} + \frac{35}{2}$

$\frac{8}{2} + \frac{6 n}{2} - \frac{8}{2} - \frac{5 n}{2} = \frac{5 n}{2} + \frac{35}{2} - \frac{8}{2} - \frac{5 n}{2}$

$\frac{n}{2} = \frac{27}{2}$

$\frac{2 n}{2} = 2 \cdot \frac{27}{2}$

$n = 27$