Question 307073
If you add x red marbles to the jar, then there will be 
50+x red marbles, and 110 + x total marbles.  If the final probability is to be 2/3, then solve this equation:


{{{(50+x)/(110+x) = 2/3}}}


Since {{{a/b=c/d }}} means that {{{ad=bc}}},
{{{(50+x)/(110+x)=2/3}}} means that {{{3(50+x)=2(110+x)}}}
{{{150 + 3x=220+ 2x}}}


Subtract 2x from each side:
{{{150+x= 220}}}


Subtract 150 from each side:
{{{x= 70}}}


Check:  You now have 50+70=120 red marbles, and 110 + 70= 180 total marbles.
The probability of getting a red  marble is {{{120/180=2/3}}}.


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus