Question 624877
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.
{{{((n+1))/((d-2))}}} = {{{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
:
{{{3/8}}} 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."
{{{((3+1))/((8-2))}}} = {{{4/6}}} which is {{{2/3}}}