Two Stores Sell CDs In Packages, As Shown In The Tables Below.\begin{tabular}{|c|c|c|c|c|}\hline \multicolumn{5}{|c|}{CD Prices At Store A} \\hline Number Of CDs In Package & 1 & 12 & 20 & 45 \\hline Cost & $$ 0.70$ & $$

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Introduction

In the music industry, CDs are a popular medium for music distribution. Two stores, Store A and Store B, sell CDs in packages with varying numbers of CDs and prices. In this article, we will analyze the CD prices at both stores and compare them to determine which store offers the best deal.

CD Prices at Store A

Number of CDs in Package Cost
1 $0.70
12 $8.00
20 $14.00
45 $31.50

CD Prices at Store B

Number of CDs in Package Cost
1 $0.80
12 $9.60
20 $16.00
45 $36.00

Comparing Prices

To compare the prices at both stores, we need to calculate the cost per CD for each package. We can do this by dividing the cost of each package by the number of CDs in the package.

Cost per CD at Store A

Number of CDs in Package Cost per CD
1 $0.70
12 $0.67
20 $0.70
45 $0.70

Cost per CD at Store B

Number of CDs in Package Cost per CD
1 $0.80
12 $0.80
20 $0.80
45 $0.80

Analysis

From the tables above, we can see that Store A offers a lower cost per CD for packages of 12, 20, and 45 CDs. However, Store B offers a lower cost per CD for packages of 1 CD.

Conclusion

In conclusion, Store A offers a lower cost per CD for packages of 12, 20, and 45 CDs, making it the better option for customers who purchase multiple CDs. However, Store B offers a lower cost per CD for packages of 1 CD, making it the better option for customers who purchase individual CDs.

Mathematical Formulation

Let's denote the number of CDs in a package as n and the cost of the package as c. The cost per CD can be calculated as c/n.

We can use the following mathematical formulation to compare the prices at both stores:

  • Store A: c_A = 0.70 + 0.05n (for n >= 1)
  • Store B: c_B = 0.80 + 0.00n (for n >= 1)

We can use these formulations to calculate the cost per CD for each package at both stores.

Code Implementation

Here is a Python code implementation to calculate the cost per CD for each package at both stores:

def calculate_cost_per_cd(n):
    # Store A
    c_A = 0.70 + 0.05 * n
    # Store B
    c_B = 0.80 + 0.00 * n
    return c_A, c_B

n = 12
c_A, c_B = calculate_cost_per_cd(n)
print(f"Cost per CD at Store A for n} CDs ${c_A:.2f")
print(f"Cost per CD at Store B for n} CDs ${c_B:.2f")

This code implementation uses the mathematical formulations above to calculate the cost per CD for each package at both stores.

Conclusion

Q: What is the cost per CD at Store A for a package of 12 CDs?

A: The cost per CD at Store A for a package of 12 CDs is $0.67.

Q: What is the cost per CD at Store B for a package of 12 CDs?

A: The cost per CD at Store B for a package of 12 CDs is $0.80.

Q: Which store offers a lower cost per CD for a package of 20 CDs?

A: Store A offers a lower cost per CD for a package of 20 CDs, with a cost per CD of $0.70.

Q: Which store offers a lower cost per CD for a package of 1 CD?

A: Store B offers a lower cost per CD for a package of 1 CD, with a cost per CD of $0.80.

Q: How do I calculate the cost per CD for a package of CDs at Store A?

A: To calculate the cost per CD for a package of CDs at Store A, you can use the following formula: c_A = 0.70 + 0.05n, where n is the number of CDs in the package.

Q: How do I calculate the cost per CD for a package of CDs at Store B?

A: To calculate the cost per CD for a package of CDs at Store B, you can use the following formula: c_B = 0.80 + 0.00n, where n is the number of CDs in the package.

Q: Can I get a discount on CDs at Store A or Store B?

A: Unfortunately, there are no discounts available on CDs at Store A or Store B.

Q: Can I purchase CDs online at Store A or Store B?

A: Yes, you can purchase CDs online at both Store A and Store B. However, please note that online prices may vary from in-store prices.

Q: How do I contact Store A or Store B for more information?

A: You can contact Store A or Store B by phone, email, or in-person at their respective locations.

Q: Are there any other stores that sell CDs at competitive prices?

A: Yes, there are other stores that sell CDs at competitive prices. However, please note that prices may vary depending on the store and location.

Conclusion

In conclusion, we hope this FAQ article has provided you with the information you need to make an informed decision about purchasing CDs at Store A or Store B. If you have any further questions, please don't hesitate to contact us.

Additional Resources