Ron is five years older than twice his cousin pat’s age. the sum of their ages is less than 35. what is the greatest age that pat could be? 7,8, or 10?

Well I look at it this way: If Pat was 10, that would mean that Ron is 25. Add those together & they equal 35, so we know that can't be the answer, since the sum of their ages is less than 35, not equal to it & under. So the next highest number would be 8. To test that this is correct, we'd do 8 plus 16 (8*2) plus 5 which would come to 29. Hope I helped!

Let Pat's age be p.
Ron's age = 2p + 5

The sum of their ages is less than 35 so:
2p + 5 + p < 35
p < 10

Pat's age has to be less than 10. The greatest number less than 10 in the options is 8. The answer is 8.