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

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

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:

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

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

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

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

$n/2= 27/2$

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

$n = 27$