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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?

Sep 10, 2021

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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

Sep 11, 2021
#2
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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.

Sep 14, 2021