SOLUTION: Linette is 3 times as old as her niece who is 4 years older than linette's daughter. If the sum of their ages is 51, how old is linette ?

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Question 1014601: Linette is 3 times as old as her niece who is 4 years older than linette's daughter. If the sum of their ages is 51, how old is linette ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Linette's age now
Let +b+ = her niece's age now
Let +c+ = Linette's daughter's age now
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(1) +a+=+3b+
(2) +b+=+c+%2B+4+
(3) +a+%2B+b+%2B+c+=+51+
--------------------
You have 3 equations and 3 unknowns,
so it's solvable
--------------------
(2) +c+=+b+-+4+
Substitute (1) and (2) into (3)
(3) +a+%2B+b+%2B+c+=+51+
(3) +3b+%2B+b+%2B+b+-+4+=+51+
(3) +5b+-+4+=+51+
(3) +5b+=+55+
(3) +b+=+11+
and
(1) +a+=+3b+
(1) +a+=+3%2A11+
(1) +a+=+33+
and
(2) +c+=+b+-+4+
(2) +c+=+11+-+4+
(2) +c+=+7+
Linette is 33
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check:
(3) +a+%2B+b+%2B+c+=+51+
(3) +33+%2B+11+%2B+7+=+51+
(3) +51+=+51+
OK