SOLUTION: If 1/8= 1/A + 1/B where A and B are different whole numbers, find the value of A+B Do this question with the fractions 1/9 and 1/10 also

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Question 1048318: If 1/8= 1/A + 1/B where A and B are different whole numbers, find the value of A+B
Do this question with the fractions 1/9 and 1/10 also
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2F8=+1%2FA+%2B+1%2FB+ ===> 1%2F8+-+1%2FA+=+1%2FB
===> B+=+%288A%29%2F%28A-8%29 ===> B+=+8%281%2B8%2F%28A-8%29%29
===> A - 8 must divide 8
===> A - 8 = 1, 2, 4, 8.
===> A = 9, 10, 12, 16
If A = 9, B = 72,
If A = 10, B = 40,
If A = 12, B = 24,
If A = 16, B = 16.
Eliminate the last possibility. (Why?)
Hence there are three possible values of A+B, namely 81, 50, and 36.
Now you can do the same for 1/9 and 1/10 also.