Carmen is 5 1/4 years younger than antoine. katy is 11 1/2 years older than carmen. to the nearest year, what is the difference in antonio age and katy age?

If Carmens age is x and Antoine is 5 1/4 years older than Carmen
then Antoine's age is x + 5 1/4
Katy is 11 1/2 years older than Carmen
hence, Katy's age is x + 11 1/2
its visible that Katy is older than Antoine since  (x + 11 1/2 ) > (x + 5 1/4)
difference between Antoine's and Katy's age can be found out by subtracting Antoine's age from Katy's age 
Difference =  Katy's age - Antoine's age 
                 = x + 11 1/2 - (x + 5 1/4)
                 = x + 11 1/2 - x - 5 1/4
                 = 6 (1/2 - 1/4)
                 = 6 1/4
6 1/4 rounded off to the nearest year is 6 years.
Therefore difference is 6 years.
Katy is 6 years older than Antoine