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

Four-fifths of my current age is also greater than five-sixths of my age one year ago.

Given that my age is an integer, what are all possible values for my age?

Explain how you determined your answer, showing all steps along the way.

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
Thus our age is in the interval

(20,30)