SOLUTION: The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by six, the simplified result is 6/7. Find the original fraction. (Do
Algebra ->
Rational-functions
-> SOLUTION: The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by six, the simplified result is 6/7. Find the original fraction. (Do
Log On
Question 1157862: The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by six, the simplified result is 6/7. Find the original fraction. (Do NOT simplify.)
You can put this solution on YOUR website! let x equal the numerator.
then x + 2 = the denominator.
your original fraction is x / (x + 2)
if you add 6 to both the numerator and the denominator, the resulting fraction is (x + 6) / (x + 8).
you are given that (x + 6) / (x + 8) = 6/7.
cross multiply to get (x + 6) * 7 = (x + 8) * 6
simplify to get 7x + 42 = 6x + 48
subtract 6x from both sides of the equation and subtract 42 from both sides of the equation to get 7x - 6x = 48 - 42
simplify to get x = 6
when x = 6, x / (x + 2) = 6/8.
when x = 6, (x + 6) / (x + 8) becomes 12 / 14 = 6/7.
the solution is confirmed to be good when x = 6.
the solution is that the original fraction is 6/8 which can be simplified to 3/4 if you so desire.
you need to simplify the equations to get the answer, however the simplified answer will not be correct if you apply the same logic.
consider.
6/8 = 12/14 when you add 6 to both numerator and denominator of the answer that is not simplified.
3/4 = 9/10 when you add 6 to both numerator and denominator of the answer that is simplified.
not simplified of 6/8 confirms the answer to be good.
simplified of 3/4 messes you up because it doesn't confirm the solution is good, even though the solution is good.
you need to use the unsimplified answer to confirm the solution is good.
i believe that's what you may have meant when you said do NOT simplify.
the unsimplified answer is 6/8.
You can put this solution on YOUR website!
The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by six, the simplified result is 6/7. Find the original fraction. (Do NOT simplify.)
Let original numerator be N
Then original denominator is N + 2
We then get:
7(N + 6) = 6(N + 8) ------- Cross-multiplying
7N + 42 = 6N + 48
7N - 6N = 48 - 42
N, or numerator = 6
Denominator: 6 + 2 = 8
Original fraction:
