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Explanation:

Total number of female members = 115

Let the number of males = x

Number of females = y

=> x + y = 115 ……(1)

According to the given data,

x + y(0.50) = 69 ……(2)

From (1) & (2), we get

0.5y = 46

=> y = 46 x 2 = 92

=> x = 115 – 92 = 23

Hence, required number of gentlemen in the family = x = 23.