Question

find the least positive integer for which the sum of its reciprocal and 9/10 is greater than 4 times the reciprocal

Answer 1

4

Explanation:

You want the least positive integer x such that ...

1/x +9/10 > 4/x

9/10 > 3/x . . . . subtract 1/x

3/10 > 1/x . . . . .divide by 3

x > 10/3 . . . . . multiply by 10x/3

The least positive integer satisfying this requirement is x = 4.