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17 May, 16:45

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

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  1. 17 May, 16:59
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    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
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