1. Elvin owns an office supply store. He charges [tex]$\$[/tex] 15.99[tex]$ per cartridge and a flat shipping fee of $[/tex]\[tex]$ 5.25$[/tex].

Which linear function models the total cost, [tex]$y$[/tex], for a single order of [tex]$x$[/tex] cartridges?

A. [tex] y = 21.24x \]

B. [tex] y = 15.99x + 5.25 \]

C. [tex] x = 21.24y \]

D. [tex] x = 15.99y + 5.25 \]



Answer :

To determine the correct linear function that models the total cost \(y\) for a single order of \(x\) cartridges at Elvin's store, we need to follow these steps:

1. Understand the Variables and Constants:
- \(x\) represents the number of cartridges ordered.
- \(y\) represents the total cost of the order.
- The flat shipping fee is fixed at \$5.25, regardless of the number of cartridges ordered.
- Each cartridge costs \$15.99.

2. Formulate the Total Cost Formula:
- Each cartridge adds \$15.99 to the total cost. If \(x\) cartridges are ordered, the cost for just the cartridges will be \(15.99 \times x\).
- In addition to the cost of the cartridges, the total cost \(y\) must also include the fixed shipping fee of \$5.25.

3. Construct the Linear Function:
- The total cost \(y\) can be modeled by adding the cost of the cartridges to the flat shipping fee.
- Thus, the function can be written as:
[tex]\[ y = 15.99x + 5.25 \][/tex]

4. Match the Formulated Function to the Given Options:
- Option A: \(y = 21.24x\): This option does not account for the separate cost per cartridge and the flat shipping fee.
- Option B: \(y = 15.99x + 5.25\): This matches the function we formulated.
- Option C: \(x = 21.24y\): This cannot be correct as it incorrectly places \(y\) as a variable when it should be the dependent variable.
- Option D: \(x = 15.99y + 5.25\): This wrongly ties the shipping cost to \(y\) and misplaces the roles of \(x\) and \(y\).

Therefore, the correct linear function that models the total cost, \(y\), for a single order of \(x\) cartridges is:
[tex]\[ \boxed{y = 15.99x + 5.25} \][/tex]

The corresponding option is [tex]\(B\)[/tex].