Answer:
Explanation:
Let's start by defining some variables. Let "p" be the cost of a poster and "c" be the cost of a comic book.
From the problem statement, we know that a poster and 3 comics cost $9.99. We can express this as:
p + 3c = 9.99
We also know that 11 comics cost $17.99. We can express this as:
11c = 17.99
Solving for "c", we get:
c = 1.63
Now we can use the first equation to solve for "p":
p + 3c = 9.99
p + 3(1.63) = 9.99
p = 4.10
So a poster costs $4.10.
The total cost of a package with x comic books and one poster can be expressed as:
y = px + 3cx
Substituting the values we found for "p" and "c", we get:
y = 4.10x + 3(1.63)x
Simplifying this equation, we get:
y = 10.99x
So the linear function rule that models the cost y of a package containing any number x of comic books is y = 10.99x.
Now let's consider the second store, which sells a similar package modeled by the linear function rule with an initial value of $6.50. This means that the cost of a package with no comic books is $6.50. We can express this as:
y = 6.50 + cx
where "c" is the cost of a single comic book.
To compare the two stores, we need to find the cost of a package with a certain number of comic books at each store. Let's say we want to compare the cost of a package with 5 comic books.
For the first store, we can use the linear function rule we derived earlier:
y = 10.99x
y = 10.99(5) = $54.95
For the second store, we can use the linear function rule:
y = 6.50 + cx
y = 6.50 + 5c
We know that the total cost of a package with 11 comic books is $17.99, so we can use this information to find "c":
11c = 17.99
c = 1.63
Now we can substitute this value of "c" into the equation for the cost of a package with 5 comic books:
y = 6.50 + 5c
y = 6.50 + 5(1.63)
y = $14.95
Therefore, the package with 5 comic books is cheaper at the second store, which sells a similar package modeled by the linear function rule with an initial value of $6.50.