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

Answer: There were 176 people in the group.

Step-by-step explanation:

Let x represent the number of people in the group.

The ratio of Yankees fans to Dodgers fans is 5 to 3. The total ratio is 5 + 3 = 8

It means that the number of Yankees fans is

5/8 * x = 5x/8

Also, the number of Dodgers fans is

3/8 * x = 3x/8

If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. It means that they would be equal. Therefore,

5x/8 - 22 = 3x/8 + 22

5x/8 - 3x/8 = 22 + 22

5x/8 - 3x/8 = 44

Multiplying both sides of the equation by 8, it becomes

5x - 3x = 352

2x = 352

x = 352/2

x = 176