- 1. The list price of an air compressor is F discount-given-to-a retailer is $$ 40 \% $$. Gom the discount method. - 2. The list price of a gas stove is P2,000 wholesaler. Find the net price using the - 3. An item with a list price of P345.75 is $$ 32 \% $$. What is the net price? You may us - 4. An electronic game listed at P180 les: offered at a further reduced price of P99 of discount was offered? - Utik Utik Distributors offers discounts on a line of products. For how much sho is to be sold for P113.40? 6. What is the list price of an article that of $$ 331 / 3 \%, 10 \% $$ and $$ 2 \% $$ if the net price

Question

UpStudy AI · Accepted Answer

It looks like you've provided a series of discount-related problems, but some of them appear to have incomplete information or formatting issues. I'll do my best to interpret and solve each problem based on the provided details. If any corrections are needed, please feel free to provide additional information.

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### **1. Air Compressor Discount**

**Problem Interpretation:**
- **List Price of Air Compressor:** $$ F $$ (Assuming $$ F $$ represents the price in pesos, ₱F)
- **Discount Given to Retailer:** $$ 40\% $$

**Solution:**
To find the **net price** after a $$ 40\% $$ discount:

$$
\text{Discount Amount} = 40\% \times F = 0.40F
$$

$$
\text{Net Price} = \text{List Price} - \text{Discount Amount} = F - 0.40F = 0.60F
$$

**Answer:** The net price of the air compressor is $$ 60\% $$ of the list price, which is $$ 0.60F $$.

---

### **2. Gas Stove Net Price**

**Problem Interpretation:**
- **List Price of Gas Stove:** ₱2,000
- **Discount Details:** *(Incomplete information; assuming a discount is given but the percentage is missing)*

**Solution:**
Since the discount percentage isn't provided, we can't calculate the net price. Please provide the discount rate to proceed.

---

### **3. Net Price After 32% Discount**

**Problem Interpretation:**
- **List Price:** ₱345.75
- **Discount:** $$ 32\% $$

**Solution:**
$$
\text{Discount Amount} = 32\% \times 345.75 = 0.32 \times 345.75 = ₱110.64
$$

$$
\text{Net Price} = \text{List Price} - \text{Discount Amount} = 345.75 - 110.64 = ₱235.11
$$

**Answer:** The net price of the item is ₱235.11.

---

### **4. Total Discount on Electronic Game**

**Problem Interpretation:**
- **Original Price:** ₱180
- **Final Price After Further Reduction:** ₱99
- **Question:** What is the total discount offered?

**Solution:**
$$
\text{Total Discount Amount} = 180 - 99 = ₱81
$$

$$
\text{Total Discount Percentage} = \left( \frac{81}{180} \right) \times 100 = 45\%
$$

**Answer:** A total discount of ₱81 was offered, which is a $$ 45\% $$ discount.

---

### **5. Selling Price After Discounts by Utik Utik Distributors**

**Problem Interpretation:**
- **Final Selling Price:** ₱113.40
- **Question:** Determine the original selling price before discounts.

**Solution:**
The problem lacks specific information about the discount rates applied. To find the original price, we need to know the total discount percentage or the sequence of discounts applied.

**Please provide the discount rates or additional details to solve this problem.**

---

### **6. Determining List Price After Multiple Discounts**

**Problem Interpretation:**
- **Successive Discounts:** $$ 33\frac{1}{3}\% $$, $$ 10\% $$, and $$ 2\% $$
- **Net Price:** *(Not provided)*

Assuming you want to find the **list price** given a **net price**, let's denote:
- **List Price:** $$ L $$
- **Net Price:** $$ N $$

**Solution:**
Calculate the cumulative effect of successive discounts:

1. **First Discount:** $$ 33\frac{1}{3}\% = \frac{1}{3} $$
   $$
   \text{After 1st Discount} = L - \frac{1}{3}L = \frac{2}{3}L
   $$

2. **Second Discount:** $$ 10\% $$
   $$
   \text{After 2nd Discount} = \frac{2}{3}L - 0.10 \times \frac{2}{3}L = 0.90 \times \frac{2}{3}L = \frac{6}{10} \times \frac{2}{3}L = \frac{6 \times 2}{10 \times 3}L = \frac{12}{30}L = \frac{2}{5}L
   $$

3. **Third Discount:** $$ 2\% $$
   $$
   \text{After 3rd Discount} = \frac{2}{5}L - 0.02 \times \frac{2}{5}L = 0.98 \times \frac{2}{5}L = \frac{196}{200} \times \frac{2}{5}L = \frac{196 \times 2}{200 \times 5}L = \frac{392}{1000}L = 0.392L
   $$

$$
N = 0.392L \Rightarrow L = \frac{N}{0.392}
$$

**Answer:** The list price $$ L $$ is equal to the net price $$ N $$ divided by $$ 0.392 $$ (i.e., $$ L = \frac{N}{0.392} $$). To find a numerical value, the net price $$ N $$ must be provided.

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**Summary:**
- **Problems 1, 3, and 4** have been addressed based on the available information.
- **Problems 2 and 5** require additional details to provide accurate solutions.
- **Problem 6** has been formulated mathematically, but a numerical answer requires the net price value.

If you can provide the missing information or clarify any parts of the problems, I'd be happy to assist further!
Cannot determine the answers without complete information for some problems.

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Solución

1. Air Compressor Discount

2. Gas Stove Net Price

3. Net Price After 32% Discount

4. Total Discount on Electronic Game

5. Selling Price After Discounts by Utik Utik Distributors

6. Determining List Price After Multiple Discounts

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