Question

What is the cost, in cents, of using a certain fax machine to send n pages of a report if the total cost for sending the first k pages is r cents and the cost for sending each additional page is s cents? (Assume that n>k)

• A. \(r + s(n - k)\)
• B. \(r + s(n + k)\)
• C. \(rs(n + k)\)
• D. \(kr + s(n - k)\)
• E. \(kr + ns\)

Hint:

Pay very close attention to the wording in problems that ask you to build formulas. "The total cost for... is r" implies a flat fee, whereas "the cost is r per page" would imply a rate to be multiplied. Option (D) is a common trap for those who misread this distinction.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem asks us to create an algebraic expression for a tiered pricing model. The total cost is the sum of the cost for the initial block of pages and the cost for the pages that exceed that initial block.
Step 2: Detailed Explanation:
1. Identify the cost for the first part.
The problem states that "the total cost for sending the first k pages is r cents". This is a flat cost for the initial block, not a per-page rate.
Cost for first k pages = \(r\).
2. Identify the cost for the additional pages.
The total number of pages is \(n\).
The number of pages covered by the initial cost is \(k\).
Therefore, the number of additional pages is \(n - k\).
The cost for each of these additional pages is \(s\) cents.
Cost for additional pages = (Number of additional pages) \(\times\) (Cost per additional page) = \((n - k) \times s\).
3. Calculate the total cost.
Total Cost = (Cost for first k pages) + (Cost for additional pages).
Total Cost = \(r + s(n - k)\).
Step 3: Final Answer:
The total cost in cents is \(r + s(n - k)\).