SOLUTION: an inheritance of $900000 is to be divided among Maria, Lorna and Fe in the following manner: Lorna is to receive 3/5 of what Maria while Fe gets 1/2 of what Maria gets. How much d

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Question 663153: an inheritance of $900000 is to be divided among Maria, Lorna and Fe in the following manner: Lorna is to receive 3/5 of what Maria while Fe gets 1/2 of what Maria gets. How much does each receive
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The fractions of the $900K that each gets
add up to +1+
Let +a+ = Maria's fraction
Let +b+ = Lorna's fraction
Let +c+ = Fe's fraction
-----------------------
given:
+b+=+%283%2F5%29%2Aa+
+c+=+%281%2F2%29%2Aa+
+a+%2B+b+%2B+c+=+1+
By substitution:
+a+%2B+%283%2F5%29%2Aa+%2B+%281%2F2%29%2Aa+=+1+
+%2810%2F10%29%2Aa+%2B+%286%2F10%29%2Aa+%2B+%285%2F10%29%2Aa+=+1+
+%2821%2F10%29%2Aa+=+1+
+a+=+10%2F21+
and
+b+=+%283%2F5%29%2Aa+
+b+=+%283%2F5%29%2A%2810%2F21%29+
+b+=+6%2F21+
and
+c+=+%281%2F2%29%2Aa+
+c+=+%281%2F2%29%2A%2810%2F21%29+
+c+=+5%2F21+
-------------
Maria receives +%2810%2F21%29%2A900000+=+428571.42+
Lorna receives +%286%2F21%29%2A900000+=+257142.85+
Fe receives +%285%2F21%29%2A900000+=+214285.71+
-------------
check:
Lorna is to receive 3/5 of what Maria gets
+257142.85+=+%283%2F5%29%2A+428571.42+
+257142.85+=+257142.85+
Fe gets 1/2 of what Maria gets
+214285.71+=+%281%2F2%29%2A428571.42+
+214285.71+=+214285.71+
and
++428571.42+%2B+257142.85+%2B+214285.71+=+900000+
+899999.98+=+900000+
I'm off by .02 due to rounding off of my calculator, I guess