In a beauty contest, half of the judges voted for miss. a .2\3 of them voted for miss. b., 10 voted for both and 6 did not vote for either miss. a or miss. b.find how many judges in all were present there

First you make the equation 1/2t+2/3t-10+6=t since the total number of Judges are the amount that voted for miss a, miss b, and neither and since 10 voted for both you have to subtract 10 so that they are not counted twice. Then you can solve for t. 1/2t+2/3t-10+6=t 7/6t-4=t -4=-1/6t t=24 Therefore the amount of judges is 24. I hope this helps.

The answer is  a) infinitely many.