# Algebra

posted by Angela

If 3 is subtracted from the numerator of a fraction, the value of the fraction is 1/2. If 6 is added to the denominator of the ORIGINAL fraction, the value of the fraction is 1/2. What is the original fraction?

1. Damon

(x-3)/y = .5

x/(y+6) = .5

-----------------

.5 y = x - 3
.5 y + 3 = x

these two equations are the same, choose any old x (infinite number of solutions)
if x = 13
.5 y = 10 so y = 20
x/y = 13/20

check that
(13 -3)/20 = 1/2 sure enough
(13)/(26) = 1/2 sure enough

2. Angela

OK, THANK YOU. But I still do not understand why x=13. that is exactly what my text uses, as well. How did you know to use 13 for x?

3. Angela

I just reworked it using your method and subsituted as you did. Then I used x=15 and got 15/24 for my final answer. However text says the correct answer is 13/20, does not say infinite number. I am thinking this is a book error! Anyway, thank you!

4. Damon

I just used 13 because I wanted easy numbers
trying x = 15 now
.5 y = 12
y = 24
so
15/24 yes
15-3/24 = 1/2 yes
15/30 = 1/2 yes
so 15/24 is just as good as 13/20

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