SOLUTION: a positive integer is 5 less than another if the reciprocal of the smaller integer is subtracted from 3 times the reciprocals of the larger than the result is 1/12
Question 1000680: a positive integer is 5 less than another if the reciprocal of the smaller integer is subtracted from 3 times the reciprocals of the larger than the result is 1/12 Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a positive integer is 5 less than another
a = b - 5
if the reciprocal of the smaller integer is subtracted from 3 times the reciprocals of the larger than the result is 1/12 - =
Replace a with (b-5) from the 1st statement - =
Multiply equation by 12b(b-5), cancel the denominators
12(3)(b-5) - 12b = b(b-5)
36a - 180 - 12b = b^2 - 5b
24a - 180 = b^2 - 5b
Form a quadratic equation on the right
0 = b^2 - 5b - 24a + 180
b^2 - 29b + 180 = 0
Factors to
(b-20)(b-9) = 0
two solutions
b = 20, then a = 15
b = 9, then a = 4
:
:
Check the first pair in the original equation - = - = Which is 1/12
:
You can check the 2nd pair in the same equation - =
