SOLUTION: this is the kind of problem that I am having trouble with: Two numbers differ by 6 and their reciprocals differ by 8/15. Find the numbers. I have been able to figure out 2 equa

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Question 387968: this is the kind of problem that I am having trouble with:
Two numbers differ by 6 and their reciprocals differ by 8/15. Find the numbers.
I have been able to figure out 2 equations based on that information:
x - y = 6 and 1/x - 1/y = 8/15
are these equations accurate?
If not, what should they be, instead?
If so, what are the next steps that I should take?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You have the right idea, but there's a slight problem.



If x%3Ey, then this means that x-y%3E0. So the first equation x-y=6 implies that x%3Ey (ie 'x' is the bigger number)


However, recall that if x%3Ey, then 1%2Fx%3C1%2Fy. So the equation 1%2Fx-1%2Fy=8%2F15 implies that 'x' is the smaller number, which is a contradiction.


So the second equation should be 1%2Fy-1%2Fx=8%2F15