SOLUTION: the denominator of a fraction is 2 more than the numerator. if both numerator and denominator are increased by 7, the simplified result is 23/24. Find the original fract

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Question 1027350: the denominator of a fraction is 2 more than the numerator.
if both numerator and denominator are increased by 7,
the simplified result is 23/24.
Find the original fraction.

X+7 / y+2+7 = 23/24
?
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
y=x+2
y-x=2>>>>>>>>>>>>>>>>>>>>(1)
(x+7)/(y+7) = 23/24
24(x+7)=23(y+7)
24x+168 =23y+161
24x-23y=-7..................(2)
Multiply eq (1) by 23
23y-23x= 46.................(3)
add (2) & (3)
x=39
y=41

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
n%2Fd, the fraction.

system%28d=2%2Bn%2C%28n%2B7%29%2F%28d%2B7%29=23%2F24%29

Do the obvious substitution.
%28n%2B7%29%2F%28n%2B2%2B7%29=23%2F24

Simplify.
%28n%2B7%29%2F%28n%2B9%29=23%2F24
24%28n%2B7%29=23%28n%2B9%29
24n%2B24%2A7=23n%2B23%2A9
24%2A7%2Bn=23%2A9
n=23%2A9-24%2A7
highlight%28n=39%29
-
highlight%28d=41%29