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
