SOLUTION: My daughter is twice is old as my son and 1/2 as old as I am. In 22 years my son will be half my age. how old is my daughter?

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Question 643220: My daughter is twice is old as my son and 1/2 as old as I am. In 22 years my son will be half my age. how old is my daughter?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = my age
Let +b+ = my Daughter's age
Let +c+ = my Son's age
given:
(1) +b+=+2c+
(2) +b+=+%281%2F2%29%2Aa+
(3) +c+%2B+22+=+%281%2F2%29%2A%28+a+%2B+22+%29+
--------------------------
(1) +c+=+b%2F2+
(2) +a+=+2b+
Substitute (1) and (2) into (3)
(3) +b%2F2+%2B+22+=+%281%2F2%29%2A%28+2b+%2B+22+%29+
multiply both sides by 2
(3) +b+%2B+44+=++2b+%2B+22++
(3) +b+=+44+-+22+
(3) +b+=+22+
My daughter is 22
check:
(1) +c+=+b%2F2+
(1) +c+=+11+
and
(2) +a+=+2%2A22+
(2) +a+=+44+
------------
(3) +11+%2B+22+=+%281%2F2%29%2A%28+44+%2B+22+%29+
(3) +33+=+%281%2F2%29%2A66+
(3) +66+=+66+