SOLUTION: Sarah's age is 1/3 of her father's age. In 13 years time her age will be 1/2 of her father's age. How old is Sarah now?

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Question 826820: Sarah's age is 1/3 of her father's age. In 13 years time her age will be 1/2 of her father's age. How old is Sarah now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Sarah's age now
Let +f+ = father's age now
+s+%2B+13+ = Sarah's age in 13 yrs
+f+%2B+13+ = father's age in 13 yrs
----------------------------------------
(1) +s+=+%281%2F3%29%2Af+
(2) +s+%2B+13+=+%281%2F2%29%2A%28f+%2B+13%29+
--------------------------------------
(1) +3s+=+f+
(2) +2%2A%28s+%2B+13%29+=+f+%2B+13+
(2) +2s+%2B+26++=+f+%2B+13+
(2) +f+-+2s+=+13+
--------------------------
Substitute (1) into (2)
(2) +3s+-+2s+=+13+
(2) +s+=+13+
Sarah is 13 now
and, since
(1) +3s+=+f+
(1) +3%2A13+=+f+
(1) +f+=+39+
check:
(2) +s+%2B+13+=+%281%2F2%29%2A%28f+%2B+13%29+
(2) +13+%2B+13+=+%281%2F2%29%2A%2839+%2B+13%29+
(2) +26+=+%281%2F2%29%2A52+
(2) +26+=+26+
OK