Home Depot wants to buy a new line of fertilizers. Manufacturer A offers a 21/13 chain discount. Manufacturer B offers a 26/8 chain discount. Both manufacturers have the same list price. What manufacturer should Home Depot buy from?

To determine which manufacturer offers the better deal for Home Depot, we need to calculate the net price Home Depot would pay after applying the chain discounts from both Manufacturer A and Manufacturer B.

### Manufacturer A: 21/13 Chain Discount
A "21/13" chain discount means that two successive discounts of 21% and 13% will be applied to the list price. Here's how you calculate the net price:
1. First discount: \( 21\% \)
   \[
   \text{Price after first discount} = (1 - 0.21) = 0.79
   \]
2. Second discount: \( 13\% \)
   \[
   \text{Price after second discount} = (1 - 0.13) = 0.87
   \]
3. Combine both discounts:
   \[
   \text{Net price factor} = 0.79 \times 0.87 = 0.6873
   \]
   So, Manufacturer A offers a net price of **68.73% of the list price**.

### Manufacturer B: 26/8 Chain Discount
For Manufacturer B, a "26/8" chain discount means successive discounts of 26% and 8%.
1. First discount: \( 26\% \)
   \[
   \text{Price after first discount} = (1 - 0.26) = 0.74
   \]
2. Second discount: \( 8\% \)
   \[
   \text{Price after second discount} = (1 - 0.08) = 0.92
   \]
3. Combine both discounts:
   \[
   \text{Net price factor} = 0.74 \times 0.92 = 0.6808
   \]
   So, Manufacturer B offers a net price of **68.08% of the list price**.

### Comparison:
- Manufacturer A: 68.73% of the list price
- Manufacturer B: 68.08% of the list price

Since **Manufacturer B** offers a lower net price (68.08%) compared to Manufacturer A (68.73%), Home Depot should buy from **Manufacturer B**.

Would you like further clarification or details?

Here are 5 follow-up questions:
1. How do you calculate chain discounts for other percentages?
2. What factors besides price might Home Depot consider when selecting a manufacturer?
3. How could these discounts impact Home Depot's profit margins?
4. How are successive discounts different from a single equivalent discount?
5. Can we use this method for more than two chain discounts?

**Tip:** Always convert percentages into decimals when performing calculations for discounts or other financial operations!

Learn how to compare chain discounts of 21/13 and 26/8 from two manufacturers to determine the best deal for Home Depot. This problem explores key mathematical concepts like percentage discounts and price comparison with detailed calculations, suitable for high school students.

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