QUESTION 22.1 A Computer Costs R14,925. If You Pay Cash, You Will Receive An $8%$ Discount.How Much Discount (in Rands) Will You Receive? (3)2.2 The Sugar Prices For The Following Bags Are As Follows: $[ \begin{array}{l} 10,
Calculating Discounts and Sugar Prices: A Mathematical Approach
In this article, we will delve into two mathematical problems that involve calculating discounts and sugar prices. The first problem requires us to find the discount amount when a computer is purchased with a cash payment, while the second problem involves finding the sugar prices for different bags. We will use mathematical concepts and formulas to solve these problems and provide step-by-step solutions.
Problem 1: Calculating the Discount on a Computer
Problem Statement
A computer costs R14,925. If you pay cash, you will receive an 8% discount. How much discount (in rands) will you receive?
Solution
To find the discount amount, we need to calculate 8% of the total cost of the computer.
Step 1: Convert the percentage to a decimal
The percentage discount is 8%. To convert this to a decimal, we divide by 100:
8 ÷ 100 = 0.08
Step 2: Multiply the total cost by the decimal
Now, we multiply the total cost of the computer (R14,925) by the decimal equivalent of the discount (0.08):
R14,925 × 0.08 = R1,194
Step 3: Calculate the discount amount
The discount amount is the result of the multiplication:
R1,194
Therefore, the discount amount is R1,194.
Problem 2: Finding Sugar Prices
Problem Statement
The sugar prices for the following bags are as follows:
| Bag Size | Price (R) |
|---|---|
| 10 kg | |
| 20 kg | |
| 50 kg |
Solution
To find the sugar prices for the different bags, we need to calculate the price per kilogram and then multiply it by the bag size.
Step 1: Find the price per kilogram
Let's assume the price per kilogram is x. We can set up an equation using the given information:
10 kg × x = 10 kg price 20 kg × x = 20 kg price 50 kg × x = 50 kg price
We can use any two equations to solve for x. Let's use the first two equations:
10 kg × x = 10 kg price 20 kg × x = 20 kg price
Divide the second equation by the first equation:
(20 kg × x) ÷ (10 kg × x) = (20 kg price) ÷ (10 kg price) 2 = 2 × (20 kg price) ÷ (10 kg price) (20 kg price) ÷ (10 kg price) = 1 20 kg price = 10 kg price
Now, we can use the first equation to find the price per kilogram:
10 kg × x = 10 kg price x = 10 kg price ÷ 10 kg x = 10 kg price per kilogram
Step 2: Find the sugar prices for the different bags
Now that we have the price per kilogram, we can find the sugar prices for the different bags:
| Bag Size | Price (R) |
|---|---|
| 10 kg | 10 kg price per kilogram × 10 kg |
| 20 kg | 10 kg price per kilogram × 20 kg |
| 50 kg | 10 kg price per kilogram × 50 kg |
Let's assume the 10 kg price is R100. Then, the price per kilogram is:
x = R100 ÷ 10 kg x = R10 per kilogram
Now, we can find the sugar prices for the different bags:
| Bag Size | Price (R) |
|---|---|
| 10 kg | R10 per kilogram × 10 kg = R100 |
| 20 kg | R10 per kilogram × 20 kg = R200 |
| 50 kg | R10 per kilogram × 50 kg = R500 |
Therefore, the sugar prices for the different bags are R100 for 10 kg, R200 for 20 kg, and R500 for 50 kg.
In our previous article, we delved into two mathematical problems that involved calculating discounts and sugar prices. In this article, we will provide a Q&A section to address some of the common questions that readers may have.
Q: What is a discount, and how is it calculated?
A: A discount is a reduction in the price of an item. It is calculated by multiplying the original price by the discount percentage.
Q: How do I calculate the discount amount?
A: To calculate the discount amount, you need to multiply the original price by the discount percentage. For example, if the original price is R14,925 and the discount percentage is 8%, the discount amount would be:
R14,925 × 0.08 = R1,194
Q: What is the difference between a discount and a sale?
A: A discount is a reduction in the price of an item, while a sale is a temporary reduction in the price of an item. A discount is usually a permanent reduction, while a sale is a temporary one.
Q: How do I calculate the price per kilogram of sugar?
A: To calculate the price per kilogram of sugar, you need to divide the total price by the number of kilograms. For example, if the total price is R100 and the number of kilograms is 10, the price per kilogram would be:
R100 ÷ 10 kg = R10 per kilogram
Q: What is the formula for calculating the price per kilogram of sugar?
A: The formula for calculating the price per kilogram of sugar is:
Price per kilogram = Total price ÷ Number of kilograms
Q: How do I find the sugar prices for different bags?
A: To find the sugar prices for different bags, you need to multiply the price per kilogram by the number of kilograms in each bag. For example, if the price per kilogram is R10 and the number of kilograms in each bag is 10, 20, and 50, the sugar prices for each bag would be:
| Bag Size | Price (R) |
|---|---|
| 10 kg | R10 per kilogram × 10 kg = R100 |
| 20 kg | R10 per kilogram × 20 kg = R200 |
| 50 kg | R10 per kilogram × 50 kg = R500 |
Q: What is the difference between a discount and a promotion?
A: A discount is a reduction in the price of an item, while a promotion is a marketing campaign that offers a discount or other incentives to customers. A promotion is usually a temporary offer, while a discount is a permanent reduction.
Q: How do I calculate the discount percentage?
A: To calculate the discount percentage, you need to divide the discount amount by the original price and multiply by 100. For example, if the discount amount is R1,194 and the original price is R14,925, the discount percentage would be:
(R1,194 ÷ R14,925) × 100 = 8%
In this article, we provided a Q&A section to address some of the common questions that readers may have about discounts and sugar prices. We hope that this article has been helpful in providing a better understanding of these mathematical concepts.