SOLUTION: The sum of age of Berma, her mother Rinna and her father Erwin is 80. Two years from no, Rinna's age will be 13 less than the sum of Erwin's age and twice Berna's age. Three years

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Question 1088169: The sum of age of Berma, her mother Rinna and her father Erwin is 80. Two years from no, Rinna's age will be 13 less than the sum of Erwin's age and twice Berna's age. Three years ago, 15 times Berma's age was 5 less than the age of Rinna. How old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let their present ages be b, r, and e
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(1) +b+%2B+r+%2B+e+=+80+
(2) +r+%2B+2+=+%28+e+%2B+2+%29+%2B+2%2A%28+b+%2B+2+%29+-+13+
(3) +15%2A%28+b+-+3+%29+=+%28+r+-+3+%29+-+5+
----------------------------------------
There are 3 unknowns and 3 equations,
so it is solvable
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(2) +r+%2B+2+=+e+%2B+2+%2B+2b+%2B+4+-+13+
(2) +2b+-+r+%2B+e+=++-+4+%2B+13+
(2) +2b+-+r+%2B+e+=+9+
---------------------------
Add (1) and (2)
(1) +b+%2B+r+%2B+e+=+80+
(2) +2b+-+r+%2B+e+=+9+
------------------------
+3b+%2B+2e+=+89+
+2e+=+89+-+3b+
+e+=+%281%2F2%29%2A%28+89+-+3b+%29+
------------------------
(3) +15%2A%28+b+-+3+%29+=+%28+r+-+3+%29+-+5+
(3) +15b+-+45+=+r+-+8+
(3) +15b+-+r+=+37+
(3) +r+=+15b+-+37+
---------------------------
Plug the last 2 results back into (1)
(1) +b+%2B+r+%2B+e+=+80+
(1) +b+%2B+15b+-+37+%2B+%281%2F2%29%2A%28+89+-+3b+%29+=+80+
(1) +16b+%2B+%281%2F2%29%2A%28+89+-+3b+%29+=+80+%2B+37+
Multiply both sides by 2
(1) +32b+%2B+89+-+3b+=+2%2A117+
(1) +29b+=+234+-+89+
(1) +29b+=+145+
(1) +b+=+5+
--------------------
(3) +r+=+15b+-+37+
(3) +r+=+15%2A5+-+37+
(3) +r+=+75+-+37+
(3) +r+=+38+
----------------------
+e+=+%281%2F2%29%2A%28+89+-+3b+%29+
+e+=+%281%2F2%29%2A%28+89+-+3%2A5+%29+
+e+=+%281%2F2%29%2A74+
+e+=+37+
----------------
Berma is 5
Rinna is 38
Erwin is 37
----------------
check:
(1) +b+%2B+r+%2B+e+=+80+
(1) +5+%2B+38+%2B+37+=+80+
(1) +80+=+80+
OK