Marcus has 20 comic books and gives 3 to his cousin Leila every week. Mike has 10 comic books and buys 2 new ones each week.

A. How many comic books will Marcus have after w weeks?

B. How many comic books will Mike have after w weeks?

C. Write an equation that represents Marcus and Mike having the same number of comic books after w weeks.

D. Solve your equation to find after how many weeks the two boys will have the same number of comic books. Check your solution.

A. After w weeks, the number of comics Marcus will have is comics.

B.after w weeks, the number of comics Mike will have is comics.

C. an equation that represents Marcus and Mike having the same number of comic books after w weeks : .

D. After two weeks, the two boys will have the same number of comic books.

Step-by-step explanation:

Step 1:

Markus has 20 comics. So the constant for the equation is 20. If he gives 3 to his cousin Leila every week then

after 1 week, the number of comics Marcus has comics,

after 2 weeks, the number of comics Marcus has comics,

after w weeks, the number of comics Marcus will have is comics. This answers option A.

Step 2:

Mike has 10 comics. So the constant for the equation is 10. If he buys 2  new ones every week then

after 1 week, the number of comics Mike has comics,

after 2 weeks, the number of comics Mike has comics,

after w weeks, the number of comics Mike will have is comics. This answers option B.

Step 3:

To write an equation that represents Marcus and Mike having the same number of comic books after w weeks we equate both the above equations.

So the equation is , this answers option C.

If we solve this equation, we get

So after two weeks, the two boys will have the same number of comic books.

To check, we substitute the values.

after 2 weeks, the number of comics Marcus will have is comics and after 2 weeks, the number of comics Mike will have is comics. So the solution is correct. This answers option D.

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