SOLUTION: The ratio of the numerator to the denominator of a certain fraction is 1 to 4. If 3 is added to the numerator and subtracted from the denominator, the new fraction reduces to {{{1

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of the numerator to the denominator of a certain fraction is 1 to 4. If 3 is added to the numerator and subtracted from the denominator, the new fraction reduces to {{{1      Log On


   

Question 186870: The ratio of the numerator to the denominator of a certain fraction is 1 to 4. If 3 is added to the numerator and subtracted from the denominator, the new fraction reduces to 1%2F3. Find the original fraction? How and what do I do to answer the above question? I am really lost on equations like these. Can you help me?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of the numerator to the denominator of a certain fraction is 1 to 4. If 3 is added to the numerator and subtracted from the denominator, the new fraction reduces to 1%2F3. Find the original fraction? How and what do I do to answer the above question? I am really lost on equations like these. Can you help me?

Let N = the numerator
Let D = the denominator

Then 

Fraction = N%2FD

The ratio of the numerator to the denominator
of a certain fraction is 1 to 4.

So

N%2FD=1%2F4

If 3 is added to the numerator and subtracted
from the denominator, the new fraction reduces to 1/3

%28N%2B3%29%2F%28D-3%29=1%2F3

So we have the system of equations:

system%28N%2FD=1%2F4%2C%28N%2B3%29%2F%28D-3%29=1%2F3%29

Cross multiply the first equation:

D=4N

Cross multiply the second equation:

D-3=3%28N%2B3%29
D-3=3N%2B9
D=3N%2B12

Now the system is simply:

system%28D=4N%2CD=3N%2B12%29

4N=3N%2B12

N=12

D=3N%2B12=3%2812%29%2B12=36%2B12=48

So the original fraction was N%2FD=12%2F48

Checking:

12%2F48 is in the ratio of 1 to 4 since it reduces to 1%2F4

Now let's add 3 to the numerator 12 and get 15
and let's subtract 3 from the denominator 48 and get 45.
Then we should have a fraction that reduces to 1%2F3

Checking:

15%2F45=1%2F3

So we are correct.  The desired fraction is 12%2F48

Edwin