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?

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)