SOLUTION: The difference between two numbers is 8 and twice the sum of their reciprocols is equal to 3 times the difference of their recipricols. Find the numbers.

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Question 946701: The difference between two numbers is 8 and twice the sum of their reciprocols is equal to 3 times the difference of their recipricols. Find the numbers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let the two numbers be a & b
:
Write an equation for each statement
:
The difference between two numbers is 8
a - b = 8
a = b + 8
and twice the sum of their reciprocals is equal to 3 times the difference of their reciprocals.
2%28%281%2Fa%29%2B%281%2Fb%29%29 = 3%28%281%2Fa%29-%281%2Fb%29%29
distribute
%282%2Fa%29%2B%282%2Fb%29 = %283%2Fa%29-%283%2Fb%29
collect like terms
%282%2Fb%29%2B%283%2Fb%29 = %283%2Fa%29-%282%2Fa%29
5%2Fb = 1%2Fa
Cross multiply
1b = 5a
replace a with (b+8) from the 1st statment
b = 5(b+8)
b = 5b + 40
-40 = 5b - b
-40 = 4b
b = -10
then
a = -10 + 8
a = -2
:
the numbers: -2 & -10
:
:
See if that works
2%28%281%2F%28-2%29%29%2B%281%2F%28-10%29%29%29 = 3%28%281%2F%28-2%29%29-%281%2F%28-10%29%29%29
2%28%285%2F%28-10%29%29%2B%281%2F%28-10%29%29%29 = 3%28%285%2F%28-10%29%29-%281%2F%28-10%29%29%29
2%28-6%2F10%29 = 3%28-4%2F10%29
-12%2F10%29 = -12%2F10%29