To make this problem simple, let's make Pat's age be 'a' for age.
So is Ron is 5 years older than double a, Ron is 2a+5 years old.
If their ages added together are less that 35 we have a + 2a + 5 < 35
Simplifying by collecting like terms, 3a +5 < 35
and subtracting 5 from each side, 3a<30
dividing each side by 3, a<10
So the greatest age Pat could be is infact 9 (as his age has to be less than 10)
