The net price of an item after trade discounts of 32.00%, 14.50%, and 5.50% is $3,600.00.

**a.** Calculate the regular selling price of the goods.

Round to the nearest cent

**b.** Calculate the equivalent discount rate of the series of discount rates.


%

Round to two decimal places

Let's solve each part of the problem step by step.

### Part (a): Calculate the Regular Selling Price

Given the net price is $3,600 after three trade discounts of 32.00%, 14.50%, and 5.50%, we need to find the regular selling price.

Let the regular selling price be $ P $.

1. **Apply the first discount (32.00%):**

   The price after the first discount:
   \[
   P_1 = P \times (1 - 0.32) = P \times 0.68
   \]

2. **Apply the second discount (14.50%):**

   The price after the second discount:
   \[
   P_2 = P_1 \times (1 - 0.145) = P \times 0.68 \times 0.855
   \]

3. **Apply the third discount (5.50%):**

   The net price after all three discounts:
   \[
   3600 = P_2 \times (1 - 0.055) = P \times 0.68 \times 0.855 \times 0.945
   \]

   Solving for $ P $:
   \[
   P = \frac{3600}{0.68 \times 0.855 \times 0.945}
   \]

   Let's calculate this:

   \[
   P = \frac{3600}{0.5488} \approx 6558.86
   \]

So, the regular selling price of the goods is **$6,558.86**.

### Part (b): Calculate the Equivalent Discount Rate

The equivalent discount rate is the single discount that would give the same net price as the series of discounts.

1. The combined discount factor from all three discounts:
   \[
   \text{Combined Discount Factor} = 0.68 \times 0.855 \times 0.945 \approx 0.5488
   \]

2. The equivalent discount rate $ r $ is:
   \[
   r = 1 - 0.5488 \approx 0.4512
   \]

   Convert to percentage:
   \[
   r \approx 45.12\%
   \]

So, the equivalent discount rate is **45.12%**.

Would you like further explanation or have additional questions?

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Here are 8 related questions to consider:

1. What would the net price be if only a single 32.00% discount was applied to the regular price?
2. How does the net price change if the order of applying the discounts is reversed?
3. How would the equivalent discount rate change if an additional 10% discount was applied after the 5.50% discount?
4. What would the regular selling price be if the net price after the discounts was $4,000 instead of $3,600?
5. What is the impact of increasing the first discount from 32.00% to 35.00% on the equivalent discount rate?
6. How does a 5.50% discount compare to a 5.00% discount in terms of the final net price?
7. What would be the net price if only the first two discounts (32.00% and 14.50%) were applied?
8. How would the equivalent discount rate change if the regular price increased by 5%?

**Tip:** When dealing with multiple discounts, always apply each discount sequentially to get an accurate final price, and use the combined discount factor to find an equivalent single discount rate.

Learn how to calculate the regular selling price of goods after multiple trade discounts and determine the equivalent discount rate. This problem involves applying sequential discounts and finding a combined discount factor. Suitable for high school students studying percentages and discounts.

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