SOLUTION: A business is owned by 3 men and 1 women, each of whom has an equal share . If one of the men sells 1/2 of his share to the woman, and another of the men keeps 2/3 of his share a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A business is owned by 3 men and 1 women, each of whom has an equal share . If one of the men sells 1/2 of his share to the woman, and another of the men keeps 2/3 of his share a      Log On


   

Question 252899: A business is owned by 3 men and 1 women, each of whom has an equal share . If one of the men sells 1/2 of his share to the woman, and another of the men keeps 2/3 of his share and sells the rest to the woman, what fraction of the business will the woman own ?
(A) 5/24 (B) 11/24 (C) 1/2 (D) 13/24 (E) 11/6
Found 2 solutions by Theo, checkley77:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
woman has 1/4 of the business.

each man has 1/4 of the business.

one man gives woman 1/2 * 1/4 = 1/8.

another man gives woman 1/3 * 1/4 = 1/12.

woman has 1/4 + 1/8 + 1/12 of the business.

LCD (least common denominator) appears to be 24.

1/4 * 6/6 = 6/24
1/8 * 3/3 = 3/24
1/12 * 2/2 = 2/24

woman has 6/24 + 3/24 + 2/24 = 11/24 of the business.

you can confirm this easily by assuming the business is worth 24 units.

each has 1/4 which means each owns 6 units.

woman has 6 units.

one man gives her 1/2 of 6 = 3 units.

another man gives her 1/3 of 6 = 2 units.

the woman now owns 6 + 3 + 2 = 11 units out of the 24.

your answer would be selection B (11/24).


Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
The woman starts with 1/4 share & each of the three men start with 1/4 share.
Thus the woman's share increases by:
1/4+1/2*1/4+1/3*1/4
1/4+1/8+1/12 now find a common denominator & add.
(6+3+2)/24=11/24 is the woman's final shares.
ANSWER B).