To solve this, we need to calculate the total price Bob’s Sporting Goods pays after applying a chain discount of 5/3/2 to the total list price of $643.

Step-by-step solution:

1. List Price:
   The total list price is $643. This is before any discounts are applied.

2. First Discount (5%):
   Apply the first discount of 5% to the list price.
   $\text{First discount} = 643 \times \frac{5}{100} = 32.15$ Subtract this discount from the list price:
   $\text{New price} = 643 - 32.15 = 610.85$

3. Second Discount (3%):
   Apply the second discount of 3% to the new price:
   $\text{Second discount} = 610.85 \times \frac{3}{100} = 18.33$ Subtract this discount from the new price:
   $\text{New price} = 610.85 - 18.33 = 592.52$

4. Third Discount (2%):
   Apply the third discount of 2% to the new price:
   $\text{Third discount} = 592.52 \times \frac{2}{100} = 11.85$ Subtract this discount from the new price:
   $\text{Final price} = 592.52 - 11.85 = 580.67$

Final Price:

After applying the chain discount, the total price Bob’s Sporting Goods will pay is $580.67.

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Would you like more details or clarifications on any part of this solution?

Here are some related questions:

1. How are chain discounts typically structured in sales?
2. What is the difference between a single and a chain discount?
3. How do you calculate multiple percentage discounts on a product?
4. How would rounding affect the final price in a multi-discount scenario?
5. What are common mistakes when applying sequential discounts?

Tip: When applying chain discounts, always calculate each discount based on the new price after the previous discount.