SOLUTION: One number is 5 times another. If the sum of their reciprocal is 6/35, find the two numbers.

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Question 57369: One number is 5 times another. If the sum of their reciprocal is 6/35, find the two numbers.
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be a and b.
a = 5b One number is 5 times another.
1%2Fa+%2B+1%2Fb+=+6%2F35 The sum of their reciprocals is 6%2F35 Simplifying this:
%28a%2Bb%29%2Fab+=+6%2F35 Cross-multiply.
35a+%2B+35b+=+6ab Substitute a = 5b.
175b+%2B+35b+=+30b%5E2 Simplify.
210b+=+30b%5E2
30b%5E2+-+210b+=+0 Factor out a b.
b%2830b+-+210%29+=+0 Apply the zero product principle.
b+=+0 and/or 30b+-+210+=+0
b+=+0 Discard this solution as not meaningful.
30b+-+210+=+0 Add 210 to both sides.
30b+=+210 Divide both sides by 30.
b+=+7
a+=+5b
a+=+35
The two numbers are:
7 and 35
Check:
1%2F7+%2B+1%2F35+=+5%2F35+%2B+1%2F35 = 6%2F35
35+=+5%287%29