So we have Kent:Mike at 7:3. We also have Mike:Zam at 6:5. We can bring these into comparable ratios by doubling Kent:Mike, so we have
Kent:Mike:Zam at 14:6:5. This says that, for every set of (14+6+5) = 25 cards, Kent owns 14, Mike has 6, and Zam has 5.
Now, we have 575 total cards, which is (575 / 25) = 23 sets of 25 cards. Kent owns (23*14) = 322 of them, Mike owns (23*6) = 138, and Zam owns (23*5) = 115.
Finally, then, Kent owns 322 - 115 = 207 more cards than Mike does.