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10 March, 03:43

Tom currently has 5 comic books in his collection and has subscribed to receive 5 new comic books each month. His uncle has 145 comic books, but sends

five to each of his 3 nieces each month. In how many months will they have the same number of comic books? How many books will that be?

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  1. 10 March, 03:54
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    After 5.6 weeks they will have the same number of comic books.

    Number of books = 61

    Step-by-step explanation:

    Tom currently has 5 comic books in his collection and has subscribed to receive 5 new comic books each month.

    Again, his uncle has 145 comic books but sends five to each of his 3 nieces each month.

    As Tom is one of his nieces so, in every week the collection of tom gets increases by (5 + 5) = 10

    Therefore, after w weeks tom's collection will have C₁ = 5 + 10w ... (1)

    And Tom's uncle will have after w weeks C₂ = 145 - 15w ... (2) comic books in his collection.

    If C₁ = C₂, then

    5 + 10w = 145 - 15w

    ⇒ 25w = 140

    ⇒ w = 5.6 weeks.

    Therefore, after 5.6 weeks they will have the same number of comic books. (Answer)

    And the number of books it will be

    C = 5 + 10 * 5.6 = 61. (Answer)
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