SOLUTION: Two numbers; the first number is 5 times the second number. If the sum of their reciprocal is 6/35, what are the two numbers?

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Question 1060534: Two numbers; the first number is 5 times the second number. If the sum of their reciprocal is 6/35, what are the two numbers?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the larger number
Let +b+ = the smaller number
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(1) +a+=+5b+
(2) +1%2Fa+%2B+1%2Fb+=+6%2F35+
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Substitute (1) into (2)
(2) +1%2F%285b%29+%2B+1%2Fb+=+6%2F35+
Multiply both sides by +5b+
(2) +1+%2B+5+=+30b%2F35+
(2) +6%2A35+=+30b+
(2) +30b+=+210+
(2) +b+=+7+
and
(1) +a+=+5b+
(1) +a+=+5%2A7+
(1) +a+=+35+
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The 1st number is 35
The 2nd number is 7
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check:
(2) +1%2Fa+%2B+1%2Fb+=+6%2F35+
(2) +1%2F35+%2B+1%2F7+=+6%2F35+
(2) +1%2F35+%2B+5%2F35+=+6%2F35+
(2) +6%2F35+=+6%2F35+
OK