Mathematics

Question

a store sells packages of comic books with a poster.


1 poster + 6 comics = $12.75
Or
1 poster + 13 comics = $19.75


a. write a linear function in the form y=mx+b that represents the cost, y, of a package containing any number of comic books.


b. Construct Arguments. Suppose another store sells a similar package, modeled by a linear function with initial value $7.99 which store has the better deal? Explain.

1 Answer

  • Answer:

    a) [tex]y=m+6.75[/tex] where [tex]m[/tex] is the number of comic books

    b) Case B has better deal  

    Step-by-step explanation:

    a)

    • Let the cost of a poster be [tex]b[/tex] ;
    • Let the cost of a comic book be [tex]x[/tex];
    • Let the number of comic books be [tex]m[/tex];
    • Let the total cost be [tex]y[/tex];

    Thus, this is in the form of :

    [tex]y=m*x+b[/tex]

    Given :

    • [tex]12.75=6*x+b[/tex]
    • [tex]19.75=13*x+b[/tex]

    subtracting both ,

    • [tex]7=7x\\x=1;[/tex]

    The cost of one comic book is $1;

    substituting in the first equation ,

    [tex]12.75=6+b\\b=6.75;[/tex]

    The equation is :

    [tex]y=m+6.75[/tex]

    b)

    Since the shop sells poster with a comic book , initial value is the cost of one comic book plus one poster.

    [tex]7.99=x+b\\x=1;[/tex] --since its similar.

    In case of a. , The cost of one book plus poster = $1+6.75=$7.75

    which is lesser than $7.99 .

    Thus case B has the best deal.  

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