Question

The cost \(c\) of an order of \(n\) special envelopes is given by \(c = ($0.50)n + $15.00\).
Column A: The cost of an order of 500 special envelopes
Column B: $260

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

Linear cost models often have a variable component (cost per item) and a fixed component (a flat fee). Make sure to calculate the total variable cost first before adding the fixed cost.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires us to use a given linear equation to calculate a specific value (the cost for 500 envelopes) and then compare it to another value.
Step 2: Key Formula or Approach:
The formula for the cost is provided: \(c = 0.50n + 15.00\). We need to substitute \(n = 500\) into this formula.
Step 3: Detailed Explanation:
We are asked to find the cost of an order of 500 special envelopes. Here, \(n = 500\).
Substitute this value into the cost equation:
\[ c = (0.50)(500) + 15.00 \]
First, calculate the variable cost part:
\[ (0.50)(500) = \frac{1}{2} \times 500 = 250 \]
Now, add the fixed cost:
\[ c = 250 + 15.00 = 265 \]
So, the cost for 500 envelopes is $265.
The quantity in Column A is $265.
The quantity in Column B is $260.
Step 4: Final Answer:
Comparing the two quantities, we have \($265>$260\). Therefore, the quantity in Column A is greater.