SOLUTION: One number is twice another. The sum of their reciprocals is 3/28. Find the numbers. These two numbers are?

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Question 130559: One number is twice another. The sum of their reciprocals is 3/28. Find the numbers. These two numbers are?
Answer by solver91311(24713) About Me  (Show Source):
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One number is twice another: x=2y
The sum of their reciprocals is 3%2F28: %281%2Fx%29%2B%281%2Fy%29=3%2F28

Step 1, substitute:


Step 2, apply common denominator:


Step 3, add the fractions:
cartoon%28red%28%281%2B2%29%29%2F2y=3%2F28%2Cred%283%29%2F2y=3%2F28%29

Step 4, since the numerators of these two equal fractions are equal, the denominators must also be equal:
cartoon%28red%283%29%2F2y=red%283%29%2F28%2C2y=28%29

Step 5, solve:
cartoon%282y%2Fred%282%29+=+28%2Fred%282%29%2Cy=14%29

Step 6, substitute derived value for y into x=2y
cartoon%28x=red%282y%29%2Cx=red%282%2A14%29%2Cx=red%2828%29%29

Check your answer:
28+=+2%2A+14
cartoon%281%2F28%2Bred%281%2F14%29=3%2F28%2C1%2F28%2Bred%282%2F28%29=3%2F28%29 Answer checks.