SOLUTION: An inheritance of 900,000 is to be divided among Scott, Alice, and Tricia in the following manner: Alice receives 3/4 of what Scott gets while Tricia receives 1/2 of what Scott ge

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Question 51628: An inheritance of 900,000 is to be divided among Scott, Alice, and Tricia in the following manner:
Alice receives 3/4 of what Scott gets while Tricia receives 1/2 of what Scott gets. How much does each receive?
Found 2 solutions by checkley71, rchill:
Answer by checkley71(8403) About Me  (Show Source):
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S+3/4*S+1/2*S=900,000 OR 9/4*S=900,000 OR 9S=3,600,000 OR S=3,600,000/9 OR S=400,000 THEN 3/4*400,000=300,000 THEN 1/2*400,000=200,000 400,000+300,000+200,000=900,000 OR 900,000=900,000

Answer by rchill(405) About Me  (Show Source):
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Let the variable x represent Scott's portion. Then, %283%2F4%29x is what Alice received and Tricia got %281%2F2%29x. We have to add all three together to get the total: x%2B%281%2F2%29x%2B%283%2F4%29x=900000. Multiplying both sides by 4 produces 4x%2B2x%2B3x=3600000, which reduces to 9x=3600000. Dividing both sides by 9 yields x=400000, which represents the amount of money that Scott recieved. Alice got 3%2F4 of that, or 3%2F4%2A400000. That reduces to 300000. Tricia got 1%2F2 of Scott, which is represented by 1%2F2%2A400000, which equates to 200000. Adding up these three amounts (400,000 + 300,000 + 200,000) gets us to 900,000 inheritance.