At an international dinner 1/5 of the people attending were french men. if the number of french women at the dinner was 2/3 greater than the number of french men and there were no other french people at the dinner then what fraction of the people at the dinner were not french?
Solution - let french men be x
so, 1/5 of the people attending french men = 1/5x
and french women greater than french men = x+2/3 => 5x/3
Unless "two-thirds greater in number" means the same thing as "two-thirds of one human being", you cannot have "2/3" stand for "2/3 more than". Also, x + 2/3 does not equal x + (2/3)x = (5/3)x = 5x/3. Did you perhaps mean "2/3" to be "(2/3)x"? If so, then your reasoning is valid.
(But, as in the other recent exercise, it would be wise to start writing what you mean. Otherwise, and especially on more complex exercises, you'll only end up confusing yourself.)
You are not asked for the number of people, so you do not need a variable for the unknown number. You are asked only for a fraction of that total number. You are given that one-fifth are French men. So what
fraction are
not French men? (Hint: Subtract.)
You are told that the number of French women is two-thirds greater than the one-fifth that are French men. What is two-thirds of one-fifth? (Hint: Multiply.) What then is two-thirds
more than one-fifth? (Hint: Add.) Then what fraction is left, which are those persons who are not French? (Hint: Subtract.)
