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?

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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?

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Answer 1 · 2016-11-09T22:26:43

$\frac{4 + 3 n}{n + 7} = \frac{5}{2}$ $(4 + 3n)/(n + 7) = 5/2$ solved is $n = 27$ $n = 27$

Explanation:

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

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

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

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

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

"the result is" is $=$ $=$

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

So, combining this all together gives:

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

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

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

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

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

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

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

$\frac{2 n}{2} = 2 \cdot \frac{27}{2}$ $(2n)/2 = 2 * 27/2$

$n = 27$ $n = 27$

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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?

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