SOLUTION: The smaller of two number is two-thirds of the larger, & the sum of their reciprocals is 1/6. What are the numbers?

Question 97184: The smaller of two number is two-thirds of the larger, & the sum of their reciprocals is 1/6. What are the numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The smaller of two numbers is two-thirds of the larger,
One number = x; smaller number =
:
the sum of their reciprocals is 1/6.
+ =
:
What are the numbers?
:
The common denominator would be 6x, multiply equation by 6x
6x* + 6x* = 6x*
:
Cancel the denominators leaving:
6(1) + 3(3) = x(1)
6 + 9 = x
x = 15 is one number
:
The smaller:
*15 = 10
:
:
Check solution in original equation:
+ =
+ =
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