SOLUTION: The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator, the fraction would become 2/3. Find the fraction.
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Question 41451: The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator, the fraction would become 2/3. Find the fraction.
This is what I have done :-
Let the denominator to be n
n–5/n and now add 1 to both the numerator and the denominator
Therefore, n-5+1/n+1 = n-4/n+1=2/3
n-4 2
___ = _
n+1 3
3(n-4) = 2(n+1)
3n-12 = 2n+2
n=12+2
n=14
Now n=14, thus denominator is n+1= 14 + 1 = 15 while numerator = n-4 = 14-4 = 10
Therefore, numerator = 10 and denominator = 15 but my teacher told us is 9 and 36 respectively instead.
I still don't really know where is / are my mistake(s). Please help.
Thank you so much. Answer by askmemath(368) (Show Source):
You can put this solution on YOUR website! You started by saying that n is the denominator
And so the numerator is n-5
Now when you solved you got the value of n = 14
which means you have to substitute this back in the orginial equation not since this fraction has had a mathematical operation performed on it
So your numerator now is 14-5 = 9
When you add 1 to the numerator 9+1 = 10
Add 1 to the denominator = 14+1 = 15
Ratio =
Yay!!
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