To achieve a 1:2 ratio of men to women at the social gathering, a specific number of couples must leave. Determining this number requires setting up and solving an equation based on the current ratio of men to women.
To have the remaining men and women in a 1:2 ratio, we first need to determine the current ratio of men to women at the gathering. Since there are 100 men and the rest are women, we have 100:((250-100)=150) or 2:3 men to women. For a 1:2 ratio, the total parts would be 1+2=3 parts. If we remove x couples (2x individuals) from the gathering, the ratio becomes (100-x):(150-2x). Setting this equal to 1:2 gives us the equation (100-x)/(150-2x) = 1/2. Solving this equation will give us the number of couples that need to leave for the ratio to be 1:2.
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