Question

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid \$3.99 for each additional compact disc purchased. If a preferred customer purchased a total of 6 compact discs and paid \$15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

• A. 5(4.00) + 15.90
• B. 5(4.00) + 15.95
• C. 5(4.00) + 16.00
• D. 5(4.00 -- 0.01) + 15.90
• E. 5(4.00 -- 0.05) + 15.95

Hint:

In questions asking for an "equivalent" expression, first calculate the definitive numerical answer from the problem's data. Then, systematically evaluate each option to see which one matches your calculated answer. Don't assume the option will look like your initial calculation steps.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The problem asks for an expression that is equivalent to the total cost of purchasing 6 compact discs under a specific discount offer. This involves calculating the actual total cost first and then evaluating the given options to find which one results in the same value.
Step 2: Detailed Explanation:
First, let's calculate the total cost based on the information provided.
The customer buys a total of 6 compact discs.
The cost of the first disc is \$15.95.
The number of additional discs is \(6 - 1 = 5\).
The cost for each additional disc is \$3.99.
The total cost for the additional discs is \(5 \times \$3.99\).
\[ 5 \times 3.99 = 19.95 \] The total cost for all 6 discs is the sum of the cost of the first disc and the cost of the additional discs.
\[ \text{Total Cost} = \$15.95 + \$19.95 = \$35.90 \] Step 3: Evaluate the Options:
Now, we need to find which of the given options is equivalent to \$35.90.
(A) \(5(4.00) + 15.90 = 20.00 + 15.90 = 35.90\)
(B) \(5(4.00) + 15.95 = 20.00 + 15.95 = 35.95\)
(C) \(5(4.00) + 16.00 = 20.00 + 16.00 = 36.00\)
(D) \(5(4.00 - 0.01) + 15.90 = 5(3.99) + 15.90 = 19.95 + 15.90 = 35.85\)
(E) \(5(4.00 - 0.05) + 15.95 = 5(3.95) + 15.95 = 19.75 + 15.95 = 35.70\)
Step 4: Final Answer:
Comparing the results, option (A) is the only expression that evaluates to \$35.90, which is the total amount the customer paid.