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.

Answer 1

a)
`y=m+6.75` where
`m` is the number of comic books

b) Case B has better deal

Explanation:

a)

• Let the cost of a poster be
  `b` ;
• Let the cost of a comic book be
  `x`;
• Let the number of comic books be
  `m`;
• Let the total cost be
  `y`;

Thus, this is in the form of :

`y=m*x+b`

Given :

• 
  `12.75=6*x+b`
• 
  `19.75=13*x+b`

subtracting both ,

• 
  `7=7x\\x=1;`

The cost of one comic book is $1;

substituting in the first equation ,

`12.75=6+b\\b=6.75;`

The equation is :

`y=m+6.75`

b)

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

`7.99=x+b\\x=1;` --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.