SOLUTION: the sum of the numerator and denominator of a fraction is 11.if 1 is added to the numerator and 2 is subtracted from the denominator,it becomes 2/3.the fraction is

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Question 624877: the sum of the numerator and denominator of a fraction is 11.if 1 is added to the numerator and 2 is subtracted from the denominator,it becomes 2/3.the fraction is
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement:
:
the sum of the numerator and denominator of a fraction is 11.
n + d = 11
n = (11-d); use this form for substitution
:
if 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3.
=
Cross multiply
3(n+1) = 2(d-2)
3n + 3 = 2d - 4
3n = 2d - 4 - 3
3n = 2d - 7
replace n with (11-d)
3(11-d) = 2d - 7
33 - 3d = 2d - 7
33 + 7 = 2d + 3d
40 = 5d
d = 40/5
d = 8
then
n = 11 - 8
n = 3
:
is the fraction
:
:
see if that checks out in the statement:
"if 1 is added to the numerator and 2 is subtracted from the denominator,it becomes 2/3."
= which is

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let the fraction =
given:
(1)
(2)
----------------------------
Multiply both sides of (2) by
(2)
(2)
(2)
------------------
Multiply both sides of (1) by
and add the equations
(1)
(2)

and, since
(1)
(1)
(1)
The fraction is 3/8
check:
(2)
(2)
(2)
(2)
OK