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 . 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 =
The ratio of the numerator to the denominator
of a certain fraction is 1 to 4.
So
If 3 is added to the numerator and subtracted
from the denominator, the new fraction reduces to 1/3
So we have the system of equations:
Cross multiply the first equation:
Cross multiply the second equation:
Now the system is simply:
So the original fraction was
Checking:
is in the ratio of 1 to 4 since it reduces to
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
Checking:
So we are correct. The desired fraction is
Edwin