Kent, Mike and Zam shared 575 cards. The ratio of the number of cards Kent had to the number of cards Mike had was of 7:3. The ratio of the number of cards Mike had to the number of cards Zam had was 6:5. How many more cards did Kent have than Zam?
Kent, Mike and Zam shared 575 cards. The ratio of the number of cards Kent had to the number of cards Mike had was of 7:3. The ratio of the number of cards Mike had to the number of cards Zam had was 6:5. How many more cards did Kent have than Zam?
K:M = 7:3 M:Z = 6:5 = 3:2.5
K:M:Z = 7:3:2.5 = 14:6:5
575/(14+6+5) = 23
K = 6 * 23 =138
Z = 5 * 23 = 115
The answer is 138 - 115 
+80 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.
