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#