Find the Fraction

Question

If 12 is subtracted from both terms of a certain fraction, the value of the fraction becomes 3/17. If 8 is added to the numerator and 6 is added to the denominator, the value of the fraction becomes 1/2. Find the fraction.

Answer 1

If 12 is subtracted from both terms of a certain fraction, the value of the fraction becomes 3/17

(x - 12)/(y - 12) = 3/17

If 8 is added to the numerator and 6 is added to the denominator, the value of the fraction becomes 1/2

(x + 8)/(y + 6) = 1/2,  x + 8 = (1/2)(y + 6)

x = [(1/2)( y + 6)] - 8

x = .5y + 3 - 8

x = .5y - 5

Substitute:

(x - 12)/(y - 12) = 3/17

(.5y - 5 -12)/(y-12) = 3/17

(.5y - 17)/(y - 12) = 3/17

(.5y - 17) = (y - 12)(3/17)

.5y - 17 = (3y - 36)/17

(17)(.5y - 17) = (3y - 36)

8.5y - 289 = 3y - 36

5.5y = 253

y = 46

x = .5y - 5 = 23 - 5 = 18

 

Hey, you better review my math!  That was quite a few manipulations...