Cassandra went to a baseball game and observed that Red Sox fans were sitting in groups of 20, while Yankees fans were sitting in groups of 15. If Cassandra saw the same total number of Yankees fans and Red Sox fans, what is the smallest number of Red Sox fans she could have observed?

Question

Mathematics

Anvil

27 February, 08:58

Cassandra went to a baseball game and observed that Red Sox fans were sitting in groups of 20, while Yankees fans were sitting in groups of 15. If Cassandra saw the same total number of Yankees fans and Red Sox fans, what is the smallest number of Red Sox fans she could have observed?

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Answers (1)

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Alice Faulkner · Answer 1

Zero! Who could possibly a Red Sox Fan when the Yankees are in town? Let them mourn the loss of the Babe forever!

Now you have a group of 20 and a group of 15. What you are being asked is what is the smallest number that you could find that can be divided evenly by 15 and 20? Is it 20 * 15=300 or is it something smaller.

The way to solve this is to write out the factors of 15 and 20.

15 = 3*5

20 = 2 * 2 * 5

So the smallest number is

one 3

two 2s

one 5 Don't count these 5s twice.

LCM = 3 * 2 * 2 * 5

LCM = 60.

The smallest group she could see of Yankee Fans and Red Sox Fans is 60 if they both must be equal.

Answer 60 Red Sox Fans.