Question

one positive number is 28 less than another number. if the reciprocal of the smaller number is added to four times the reciprocal of the larger number, the sum is 1/6. Find the two numbers

Answer 1

Let x represent the larger number.
  1/(x -28) +4/x = 1/6
Multiplying by the product of denominators, we have
  6x +24(x -28) = x(x -28)
In standard form, this is
  x^2 -58x +672 = 0
  (x -42)(x -16) = 0

The two numbers are (-12 and 16) or (14 and 42).