Apositive integer is 15 less than another. if 4 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer, then the result is − 3/4 . find all pairs of integers that satisfy this condition.

Translate the info given into equations:

A positive integer is 15 less than another   -----> x = y - 15

If 4 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer, then the result is − 3/4
------> (1/y) - (4/x) = -3/4

Use substitution, replace 'x' with 'y-15' in 2nd equation



We know that both x and y must be positive integers, so y =-1 is not a solution.

If y=20, then x = 20-15 = 5

Final
The pair of integers is (5,20)