SOLUTION: a fraction is equal to 1/2. if its numerator is increased by 1 and its denominator is increased by 5 the value of the resulting fraction is 4/9 find the original fraction

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Question 707485: a fraction is equal to 1/2. if its numerator is increased by 1 and its denominator is increased by 5 the value of the resulting fraction is 4/9 find the original fraction
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
"a fraction is equal to 1/2."
n%2Fd = 1%2F2
Cross multiply
d = 2n
:
"if its numerator is increased by 1 and its denominator is increased by 5 the value of the resulting fraction is 4/9"
%28n%2B1%29%2F%28d%2B5%29 = 4%2F9
Cross multiply
9(n+1) = 4(d+5)
9n + 9 = 4d + 20
9n = 4d + 20 - 9
9n = 4d + 11
replace d with 2n
9n = 4(2n) + 11
9n = 8n + 11
9n - 8n = 11
n = 11
then
d = 22
hence
11%2F22 is the original fraction (which = 1/2)
:
:
Check this
%2811%2B1%29%2F%2822%2B5%29 =
12%2F27 reduces to 4%2F9