Question

Four-fifths of my current age is greater than three-quarters of my age one year from now.

Answer 1

Let current age be x, next we construct the inequalities for the age:
Four-fifths of my current age is greater than three-quarters of my age one year from now.
thus when we add 1 year to 3/4 of our current age and set the inequality
4x/5>3x/4+1......i

Four-fifths of my current age is also greater than five-sixths of my age one year ago.
Thus when we subtract 1 from 5x/6 and set the inequality we get
4x/5>5x/6-1.......ii
solving the inequalities we obtain:
4x/5>3x/4+1
x/20>1
hence multiplying both sides by 20 we obtain:
x>20

also

4x/5>5x/6-1
4x/5-5x/5>-1
-x/30>-1
multiplying both sides by 30 we get:
-x>-30
thus
x<30
therefore the possible values of my age will lie in the interval:
20<x<30
Thus our age is in the interval
(20,30)