SOLUTION: Find a fraction that reduces to 3/4 either if 1 is added to the numerator or if 11 is subtracted from the numerator and the denominator is halved. Please help! Thank you!

Algebra ->  Equations -> SOLUTION: Find a fraction that reduces to 3/4 either if 1 is added to the numerator or if 11 is subtracted from the numerator and the denominator is halved. Please help! Thank you!      Log On


   

Question 701059: Find a fraction that reduces to 3/4 either if 1 is added to the numerator or if 11 is subtracted from the numerator and the denominator is halved.
Please help!
Thank you!
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let your fraction be a/b.
Then we have
(1) (a+1)/b = 3/4 and
(2) (a-11)/(b/2) = 3/4 which simplifies to
(3) 2*(a-11)/b = 3/4
Since (1) and (3) equal the same number, 3/4, we can set them equal to each other and get
(4) (a+1)/b = 2*(a-11)/b
In (4) the b cancels from each side (assuming b is not zero) leaving
(5) a+1 = 2a-22 or
(6) a = 23
Use a of (6) in (1) and get
(7) (23+1)/b = 3/4 or by cross miultiplying we get
(8) 3b = 4*24 or
(9) b = 32
Let's check the values of a and b using (2).
Is ((23-11)/(32/2) = 3/4)?
Is (12/16 = 3/4)?
Is (3/4 = 3/4)? Yes
Answer: The fraction is 23/32.