Question

Every person in a certain group is either a Dodgers fan or a Yankees fan, but not both. The ratio of Yankees fans to Dodgers fans is 5 to 3. If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. How many people are in the group?A) 22B) 88C) 128D) 144E) 176

Answer 1

176

Explanation:

E) 176

Answer 2

E) 176

Explanation:

The difference in ratio units is 5 -3 = 2. If one ratio unit changes sides, the ratio will be 4 : 4, or 1 : 1. Then one ratio unit represents 22 group members.

There are a total of 5+3 = 8 ratio units, so there are ...

8 × 22 = 176

people in the group.

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Check

The original group has 5 × 22 = 110 Yankees fans and 3 × 22 = 66 Dodgers fans, for a total of 110+66 = 176 group members. If 22 switch sides, there will be 110-22 = 88 Yankees fans and 66+22 = 88 Dodgers fans, making the ratio ...

88 : 88 = 1 : 1