A. After w weeks, the number of comics Marcus will have is[tex]20 -3w[/tex] comics.
B.after w weeks, the number of comics Mike will have is [tex]10 + 2w[/tex] comics.
C. an equation that represents Marcus and Mike having the same number of comic books after w weeks : [tex]20 -3w = 10+2w[/tex].
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 [tex]20 - 1(3) = 17[/tex] comics,
after 2 weeks, the number of comics Marcus has [tex]20 - 2(3) = 14[/tex] comics,
after w weeks, the number of comics Marcus will have is[tex]= 20 - w(3) = 20 -3w[/tex] 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 [tex]10 + 1(2) = 12[/tex] comics,
after 2 weeks, the number of comics Mike has [tex]10 + 2(2) = 14[/tex] comics,
after w weeks, the number of comics Mike will have is[tex]10 + w(2) = 10 + 2w[/tex] 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 [tex]20 -3w = 10+2w[/tex], this answers option C.
If we solve this equation, we get
[tex]20 -10 =2w+3w, 10 = 5w , w =2.[/tex]
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[tex]20 - 2(3) = 14[/tex] comics and after 2 weeks, the number of comics Mike will have is [tex]10 + 2(2) = 14[/tex] comics. So the solution is correct. This answers option D.
