Skis are listed by a manufacturer for $860, less trade discounts of 30% and 18%. What further rate of discount should be given to bring the net price to $445?
%
Round to two decimal places

To find the further rate of discount required to bring the net price to $445, let's follow these steps:

1. **Calculate the price after the first discount of 30%:**

   \[
   \text{Price after 30% discount} = 860 \times (1 - 0.30) = 860 \times 0.70 = 602
   \]

2. **Calculate the price after the second discount of 18%:**

   \[
   \text{Price after 18% discount} = 602 \times (1 - 0.18) = 602 \times 0.82 = 493.64
   \]

3. **Determine the required further discount rate to bring the price from $493.64 to $445:**

   Let $ r $ be the further rate of discount. The equation will be:

   \[
   493.64 \times (1 - r) = 445
   \]

   Solve for $ r $:

   \[
   1 - r = \frac{445}{493.64} \approx 0.9015
   \]

   \[
   r = 1 - 0.9015 \approx 0.0985
   \]

   Therefore, the further rate of discount required is approximately **9.85%**.

Would you like more details or have any other questions?

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Here are 8 related questions to consider:

1. How would the final price change if the initial discounts were applied in reverse order?
2. What would be the final price if only the first 30% discount was applied?
3. How does the order of applying discounts affect the final price?
4. How would the further discount rate change if the target net price was $400 instead of $445?
5. What is the effective discount rate after applying both 30% and 18% discounts?
6. If the manufacturer increased the initial price by 10%, what would the new further discount rate need to be?
7. How would the final price change if a single 48% discount was applied instead of the two consecutive discounts?
8. What would the required further discount rate be if the target price was $450 instead of $445?

**Tip:** When calculating consecutive discounts, remember that each discount is applied to the price obtained after the previous discount, not the original price.

Explore how to calculate the further rate of discount needed to adjust the net price to $445 after initial trade discounts of 30% and 18% on skis priced at $860. Step-by-step solution provided.

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