Discount Problems
1) Problem: Calculate total amount Lenie Rose paid after a 4% discount and find how much discount she saved.
Step 1: Calculate the total price of each item without discount.
- Calamansi juice: $6 \times 12.75 = 76.50$
- Mango piayaya: $5 \times 45 = 225$
- Mango polvoron: $5 \times 55 = 275$
Step 2: Calculate total price without discount.
$$76.50 + 225 + 275 = 576.50$$
Step 3: Calculate the discount amount at 4%.
$$0.04 \times 576.50 = 23.06$$
Step 4: Calculate the final amount paid after discount.
$$576.50 - 23.06 = 553.44$$
Answer: Lenie Rose paid **553.44** and saved **23.06** as discount.
2) Problem: Find original price of tennis shoes given that ₱1,785 was paid after 20% discount.
Step 1: Let original price be $x$.
Step 2: Price after 20% discount is 80% of original price.
$$0.80x = 1785$$
Step 3: Solve for $x$.
$$x = \frac{1785}{0.80} = 2231.25$$
Answer: The original price of the tennis shoes was **2231.25**.
3) Problem: Find discount rate given sale price ₱3,937.50 and original price ₱4,500.
Step 1: Calculate discount amount.
$$4500 - 3937.50 = 562.50$$
Step 2: Find discount rate as a percentage.
$$\frac{562.50}{4500} \times 100\% = 12.5\%$$
Answer: The rate of discount is **12.5%**.
4) Problem: Find discount Katrina gave her friend who paid ₱1,800 after 15% discount.
Step 1: Calculate discount amount.
$$0.15 \times 1800 = 270$$
Answer: Katrina gave her friend a discount of **270**.
5) Problem: Find original price and final price paid for 1 dozen hair clips, discount amount ₱26.25 at 15% discount.
Step 1: Let the original price be $x$.
Step 2: Since discount is 15%, amount discounted is:
$$0.15x = 26.25$$
Step 3: Solve for $x$.
$$x = \frac{26.25}{0.15} = 175$$
Step 4: Calculate price paid after discount.
$$175 - 26.25 = 148.75$$
Answer: Original price was **175** and they paid **148.75** for one dozen hair clips.