Question 122942
he denominator of a fraction is is 3 times the numerator. If 8 is added to the numerator and 6 is subtracted from the denominator then the value is 8/9. Find the original fraction. 
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Quite frankly, I am not sure what you are doing, but here is how I would do it
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Let x = numerator:
It says'"the denominator of a fraction is is 3 times the numerator." therefore:
3x = denominator
Our fraction:
{{{x/(3x)}}} 
Then it says,
" If 8 is added to the numerator and 6 is subtracted from the denominator then the value is 8/9." so we can write:
{{{((x+8))/((3x-6))}}} = {{{8/9}}}
Cross multiply and we have:
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8(3x-6) = 9(x+8)
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Do some basic algebra here:
24x - 48 = 9x + 72
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24x - 9x = 72 + 48
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15x = 120
x = {{{120/15}}}
x = 8
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Our original fraction: {{{8/24}}}
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Check solution in the statement
 "If 8 is added to the numerator and 6 is subtracted from the denominator then the value is 8/9."
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 {{{(8 + 8)/(24 - 6)}}}  = {{{16/18}}} =  {{{8/9}}}
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How about this? Did I makes sense to you here?