SOLUTION: wendy is 6 years younger than her brother.The product of their ages is 91.Find their ages.

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Question 884961: wendy is 6 years younger than her brother.The product of their ages is 91.Find their ages.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = Wendy's age
Let +b+ = brother's age
-----------------------
(1) +w+=+b+-+6+
(2) +w%2Ab+=+91+
-----------------
Substitute (1) into (2)
(2) +%28+b+-+6+%29%2Ab+=+91+
(2) +b%5E2+-+6b+=+91+
Complete the square
(2) +b%5E2+-+6b+%2B+%28+6%2F2+%29%5E2++=+91+%2B+%28+6%2F2+%29%5E2+
(2) +b%5E2++-+6b+%2B+9+=+91+%2B+9+
(2) +%28+b+-+3+%29%5E2+=+100+
Take the square root of both sides
(2) +b+-+3+=+10+
(2) +b+=+13+
and
(1) +w+=+b+-+6+
(1) +w+=+13+-+6+
(1) +w+=+7+
-------------------
Wendy is 7 and her brother is 13
check:
+7%2A13+=+91+
OK