SOLUTION: The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?

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Question 893959: The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?
Answer by MathTherapy(10552) About Me  (Show Source):
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The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?


Let the smaller number be S

Then larger number = 9%2FS

When the numbers become reciprocals, the smaller number becomes the LARGER reciprocal, and the

larger number becomes the SMALLER reciprocal

Thus, the larger reciprocal is: 1%2FS, and the smaller reciprocal is: 1%2F%289%2FS%29, or S%2F9

Therefore, the LARGER RECIPROCAL, equals 4 times the SMALLER RECIPROCAL, OR

1%2FS+=+4%28S%2F9%29

1%2FS+=+4S%2F9

4S%5E2+=+9 ------- Cross-multiplying

S%5E2+=+9%2F4

S, or smaller number = sqrt%289%2F4%29, or highlight_green%283%2F2%29

Larger number: 9%2F%283%2F2%29, or 9%282%2F3%29, or highlight_green%286%29



Sum of the two numbers: 3%2F2+%2B+6, or 3%2F2+%2B+12%2F2, or 15%2F2, or highlight_green%2815%2F2%29, or highlight_green%287.5%29

You can do the check!! 



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