SOLUTION: 1. A manufacturer sells kayaks to dealers for Php 94,500 with discounts of 40/10/5.
a. Determine the net price of a kayak.
b. How much is the total trade discount?
c. What is th
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Question 1168239: 1. A manufacturer sells kayaks to dealers for Php 94,500 with discounts of 40/10/5.
a. Determine the net price of a kayak.
b. How much is the total trade discount?
c. What is the equivalent single trade discount for this transaction?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let the list price of a kayak be $L = \text{Php } 94,500$.
The discounts offered are 40/10/5. This means there are three successive discounts.
**a. Determine the net price of a kayak.**
To find the net price, we apply the discounts sequentially to the original price.
1. **First discount (40%):**
Discount amount = $40\% \times 94,500 = 0.40 \times 94,500 = \text{Php } 37,800$
Price after the first discount = $94,500 - 37,800 = \text{Php } 56,700$
2. **Second discount (10%):**
This discount is applied to the price after the first discount.
Discount amount = $10\% \times 56,700 = 0.10 \times 56,700 = \text{Php } 5,670$
Price after the second discount = $56,700 - 5,670 = \text{Php } 51,030$
3. **Third discount (5%):**
This discount is applied to the price after the second discount.
Discount amount = $5\% \times 51,030 = 0.05 \times 51,030 = \text{Php } 2,551.50$
Net price = $51,030 - 2,551.50 = \text{Php } 48,478.50$
Alternatively, we can calculate the net price using the discount factors:
Net price = List price $\times (1 - \text{discount}_1) \times (1 - \text{discount}_2) \times (1 - \text{discount}_3)$
Net price = $94,500 \times (1 - 0.40) \times (1 - 0.10) \times (1 - 0.05)$
Net price = $94,500 \times (0.60) \times (0.90) \times (0.95)$
Net price = $94,500 \times 0.513$
Net price = $\text{Php } 48,478.50$
**b. How much is the total trade discount?**
The total trade discount is the difference between the original list price and the net price.
Total trade discount = List price - Net price
Total trade discount = $94,500 - 48,478.50 = \text{Php } 46,021.50$
**c. What is the equivalent single trade discount for this transaction?**
The equivalent single trade discount is the single discount rate that would give the same net price. Let the equivalent single discount rate be $d$.
Net price = List price $\times (1 - d)$
$48,478.50 = 94,500 \times (1 - d)$
$1 - d = \frac{48,478.50}{94,500}$
$1 - d = 0.513$
$d = 1 - 0.513$
$d = 0.487$
To express this as a percentage, we multiply by 100:
Equivalent single trade discount = $0.487 \times 100\% = 48.7\%$
Final Answer: The final answer is $\boxed{a. \text{Php } 48,478.50, b. \text{Php } 46,021.50, c. 48.7\%}$
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