https://file.aiquickdraw.com/mathbot/file/1726486213336niv62eg2.jpg

Let's go through the problems one by one.

### 1. Net Invoice Price Problem (Wall Clock)
The net invoice price is ₱28,827.88, and the discount granted was 18%. We need to find:
- a) Net invoice price rate
- b) List price
- c) Discount

**Solution:**
- **a) Net invoice price rate** is simply the percentage of the list price after the discount. Since the discount is 18%, the net invoice price rate would be \( 100\% - 18\% = 82\% \).

- **b) List price (P)**: The formula for net invoice price \( NIP \) is:
  \[
  NIP = P \times (1 - \text{discount rate})
  \]
  Here, \( NIP = 28,827.88 \), and the discount rate is 18% or 0.18.
  Solving for \( P \):
  \[
  28,827.88 = P \times (1 - 0.18) = P \times 0.82
  \]
  \[
  P = \frac{28,827.88}{0.82} = 35,158.39
  \]
  So, the list price is approximately ₱35,158.39.

- **c) Discount**:
  \[
  \text{Discount} = P - NIP = 35,158.39 - 28,827.88 = 6,330.51
  \]
  The discount is ₱6,330.51.

---

### 2. Dining Table Problem
The net invoice price is ₱6,187.50, which represents 75% of the original price. We need to find:
- a) Original price
- b) Discount
- c) Discount rate

**Solution:**
- **a) Original price**:
  The net invoice price \( NIP \) is given by \( NIP = 75\% \times \text{Original Price (OP)} \), which means:
  \[
  6,187.50 = 0.75 \times OP
  \]
  Solving for \( OP \):
  \[
  OP = \frac{6,187.50}{0.75} = 8,250
  \]
  So, the original price is ₱8,250.

- **b) Discount**:
  \[
  \text{Discount} = OP - NIP = 8,250 - 6,187.50 = 2,062.50
  \]
  So, the discount is ₱2,062.50.

- **c) Discount rate**:
  The discount rate is:
  \[
  \text{Discount Rate} = \frac{\text{Discount}}{OP} \times 100 = \frac{2,062.50}{8,250} \times 100 = 25\%
  \]

---

### 3. Washing Machine Problem
The washing machine is listed at ₱20,040 and is granted successive discounts of 20%, 10%, and 5%. We need to find:
- a) Net invoice price
- b) Total discount

**Solution:**
To calculate successive discounts, we multiply the list price by the complement of each discount (i.e., \( 1 - \text{discount rate} \)).

- **a) Net invoice price**:
  The successive discounts are applied as follows:
  \[
  NIP = 20,040 \times (1 - 0.20) \times (1 - 0.10) \times (1 - 0.05)
  \]
  First discount:
  \[
  20,040 \times 0.80 = 16,032
  \]
  Second discount:
  \[
  16,032 \times 0.90 = 14,428.8
  \]
  Third discount:
  \[
  14,428.8 \times 0.95 = 13,707.36
  \]
  So, the net invoice price is approximately ₱13,707.36.

- **b) Total discount**:
  The total discount is the difference between the list price and the net invoice price:
  \[
  \text{Total discount} = 20,040 - 13,707.36 = 6,332.64
  \]

---

### 4. Completing the Table
Let’s complete the missing parts of the table:

#### First row:
Original price: ₱158.75  
Discount rate: 5%  
We calculate the trade discount and net invoice price:
- **Trade Discount** = \( 158.75 \times 0.05 = 7.94 \)
- **Net Invoice Price** = \( 158.75 - 7.94 = 150.81 \)

Now, using these solutions and methods, are there any specific parts you'd like more details on or further explanations for?

### Follow-Up Questions:
1. How do we handle cases with multiple discounts applied successively?
2. What is the relationship between the discount rate and the net invoice price rate?
3. How do we calculate the total discount rate in scenarios with successive discounts?
4. Can you apply this concept to calculate the NIP for a product with two 15% discounts?
5. What is the difference between trade discount and net invoice price?

### Tip:
When handling multiple discounts, always remember to apply each discount step by step rather than summing them up, as they are calculated successively.

The net invoice price of a wall clock is ₱28,827.88. If the discount granted was 18%, find: a) net invoice price rate b) list price c) discount.

The net invoice price of a dining table is ₱6,187.50, representing 75% of the original price. Find: a) original price b) discount c) discount rate.

A washing machine listed at ₱20,040 is granted 20%, 10%, and 5% discounts. Find: a) net invoice price b) discount.

Learn how to calculate the net invoice price, list price, and discounts for products like a wall clock, dining table, and washing machine. This problem covers concepts like percentage discount and successive discount. Suitable for high school students (Grades 10-12).

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