Question

An integer is such that one-fouth of the next integer is atleast one more than one-fifth of the previous integer. Find the smallest value of the integer.

Answer 1

Let the integer be n.

`(1/4)(n + 1) ≥ 1 + (1/5)(n − 1)`

Multiply by 20: 

5(n + 1) ≥ 20 + 4(n − 1)

5n + 5 ≥ 4n + 16

n ≥ 11

So the smallest integer is 11.