SOLUTION: Find the number of pairs of natural number a and b which satisfy 1/a + 2/b = 1/18 where b is an odd natural number less than 80 ??

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Question 977076: Find the number of pairs of natural number a and b which satisfy 1/a + 2/b = 1/18 where b is an odd natural number less than 80 ??
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the number of pairs of natural number a and b which satisfy 1/a + 2/b = 1/18 where b is an odd natural number less than 80 ??
1%2Fa + 2%2Fb = 1%2F18
multiply equation by 18ab, cancel the denominators, we have
18b + 36a = ab
18b - ab = -36a
Factor out b
b(18-a) = -36a
b = %28-%2836a%29%29%2F%28%2818-a%29%29 = %28-%2836a%29%29%2F%28-1%28a-18%29%29
b = %2836a%29%2F%28a-18%29
:
I don't think there are any pairs of natural numbers (meaning positive integers) that satisfy this.
A graph of the above equation shows this
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%2836x%29%2F%28x-18%29%29+