SOLUTION: A sum of money was shared among three sisters Alice, Betty and Cathy . Alice received 30% of the total sum while Betty received 25% less than Cathy. If Betty received $225 , wha

Algebra ->  Finance -> SOLUTION: A sum of money was shared among three sisters Alice, Betty and Cathy . Alice received 30% of the total sum while Betty received 25% less than Cathy. If Betty received $225 , wha      Log On


   

Question 1164327: A sum of money was shared among three sisters Alice, Betty and Cathy . Alice
received 30% of the total sum while Betty received 25% less than Cathy. If Betty received $225 , what was the total sum of money three sisters shared??
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Betty received 25% less than Cathy --> Betty received 3/4 as much as Cathy.

Let 3x be the amount Betty received and 4x be the amount Cathy received.

The percentages the three sisters received add up to 1 (=100% = 1.00):

.30%2B3x%2B4x+=+1.00
7x+=+0.70
x+=+0.10

Betty's share was 3x = 0.30 = 30%; Cathy's share was 4x = 0.40 = 40%.

Betty's share of 30% of the total was $225; the total was $225/0.30 = $750.

ANSWER: The three sisters shared a total of $750.