The numerator and the denominator of a certain fraction are consecutive odd numbers. If nine is subtracted from the numerator then the ratio to the numerator to the denominator of the new fraction is two to three. Find the original fraction.
These problems are confusing me so bad... I have like 6 more and I've only been able to do 3 on my own. It really sucks. So I really appreciate it if you could help me in any way.
2007-07-03 08:38:33 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
original number = n / (n+2)
New number = (n-9) / (n+2)
ratio = (n-9) / (n+2) = 2/3
2n+4 = 3n - 27
n = 31
Original no = 31/33
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You could also have done it in reverse.
Start with the second number
2x / 3x
Add 9 to the numeratore
(2x+9) / (3x)
So 3x = 2x + 9 + 2
x = 11
So 2nd number = 22/33
original number = 31/33
2007-07-03 08:43:43 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
Dear Melanie,
My bad! The first step is to read the question carefully! I thought nine was subtracted from both the numerator and the denominator!
Here is the answer to the wrong question.
With problems like these, you want to start with the smallest trial numbers (11 and 13) and see if they satisfy the question. If not, work up from there. 2 and 3 only differ by one, so the smallest possible (keeping everything positive) numbers don't work in this problem, but the very next two consecutive odd numbers do work.
2007-07-03 15:55:13 · answer #2 · answered by George Fischer 2 · 0⤊ 0⤋
You need to be methodical in approach.
Let n represent the numerator.
Let d represent the denominator.
Then d - n = 2 (consecutive odd numbers)
(n - 9)/d = 2/3
Substitute for d.
(n - 9)/(n + 2) = 2/3
Cross-multiply to remove fractions.
3(n - 9) = 2(n + 2)
Remove brackets.
3n - 27 = 2n + 4
Gather like terms.
3n - 2n = 27 + 4
n = 31, so d = 33.
Proof:
Original fraction is 31/33
31 - 9 = 22, 22/33 has ratio 2/3.
2007-07-03 15:53:54 · answer #3 · answered by Robert S 7 · 0⤊ 0⤋
first number = x
second consec. odd number = x + 2
Numerator / denominator
Original fraction:
x / (x + 2)
New fraction:
(x - 9) / (x + 2) = 2 / 3
Cross multiply...
3(x - 9) = 2(x + 2)
3x - 27 = 2x + 4
x - 27 = 4
x = 31
so, x + 2 = 33
Original fraction is 31 / 33
2007-07-03 15:50:07 · answer #4 · answered by Mathematica 7 · 0⤊ 0⤋
::
(n - 9)/d = 2/3
3n - 27 = 2d
But d = n + 2, so
3n - 27 = 2(n + 2)
3n - 2n = 27 + 4
n = 31
d = 33
Similarly,
d = n - 2, so
3n - 27 = 2(n - 2)
3n - 2n = 27 - 4
n = 23
d = 21
2007-07-03 16:13:41 · answer #5 · answered by sweetwater 7 · 0⤊ 0⤋