DAY 257

FRACTIONS AND MARRIAGE
Credit: GAMES Magazine--Bill Graham

NOTE: If you can solve this problem, according to a speaker who presented it at a math conference, then you really understand fractions.

In a town, three-fifths of the women are married to two-thirds of the men. What fraction of the town's adults are married? (Marriage is defined here as one man married to one woman.)

Answer:

Twelve-nineteenths.................If m = the number of men in the town and w = the number of women, then 3/5 (w) = 2/3 (m). Multiplying both sides of the equation by 15 yields the equation 9w = 10m. The smallest whole numbers that could satisfy this equation are w = 10 and m = 9, in which case we can confirm that three-fifths of the women (6) would be married to two-thirds of the men (6). This in turn would mean that 12 of the nineteen townspeople are married. Using solutions that are multiples of 10 and 9 will not alter this fraction.