Question

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.

Answer 1

A. After w weeks, the number of comics Marcus will have is
`20 -3w` comics.

B.after w weeks, the number of comics Mike will have is
`10 + 2w` comics.

C. an equation that represents Marcus and Mike having the same number of comic books after w weeks :
`20 -3w = 10+2w`.

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

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
`20 - 1(3) = 17` comics,

after 2 weeks, the number of comics Marcus has
`20 - 2(3) = 14` comics,

after w weeks, the number of comics Marcus will have is
`= 20 - w(3) = 20 -3w` 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
`10 + 1(2) = 12` comics,

after 2 weeks, the number of comics Mike has
`10 + 2(2) = 14` comics,

after w weeks, the number of comics Mike will have is
`10 + w(2) = 10 + 2w` 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
`20 -3w = 10+2w`, this answers option C.

If we solve this equation, we get

`20 -10 =2w+3w, 10 = 5w , w =2.`

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
`20 - 2(3) = 14` comics and after 2 weeks, the number of comics Mike will have is
`10 + 2(2) = 14` comics. So the solution is correct. This answers option D.