SOLUTION: the sum of the reciprocals of two number is 5/8. four times the reciprocal of the first is twice as much as eight times the reciprocal of the second. find the numbers.

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Question 669185: the sum of the reciprocals of two number is 5/8. four times the reciprocal of the first is twice as much as eight times the reciprocal of the second. find the numbers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement; the two numbers are a & B
:
the sum of the reciprocals of two number is 5/8.
1%2Fa + 1%2Fb = 5%2F8

four times the reciprocal of the first is twice as much as eight times the reciprocal of the second.
4%281%2Fa%29 = 2%288%2Fb%29
which is
4%2Fa = 16%2Fb
cross multiply
4b = 16a
divide both sides by 4
b = 4a
:
find the numbers.
Back to the 1st equation, replace b with 4a
1%2Fa + 1%2F%284a%29 = 5%2F8
multiply by 8a, results:
8 + 2 = 5a
10 = 5a
a = 2
then
b = 4*2
b = 8
:
:
See if that checks out
1%2F2 + 1%2F8 = 5%2F8
4%2F8 + 1%2F8 = 5%2F8