Section: Math Section 1
15)
A business is owned by 9 women and 1 man, each of whom owns an equal share. If one of the women sells 1/2 of her share to the man, and another woman keeps 1/5 of her share and sells the rest to the man, what fraction of the business will the man own?
Explanation
Picking numbers makes this problem easier to work with. Rather than dealing with fractions of the business, say that there are 100 total shares. At the beginning of the problem, the 9 women each own 10 shares and the man owns 10 shares. One woman sells 1/2 of her part of the business, 5 shares, to the man, and another woman sells 1 - 1/5 = 4/5 other part of the business, 20(4/5) = 8 shares to the man. Now the man owns 10 + 5 + 8 = 23 shares out of the total 100 shares in the business or 23/100.
