Problem 71 - Elementary Algebra

Question

The original price of red bell peppers is \(\$ 2.99\) per pound. If the peppers are on sale at \(25 \%\) off, find the cost of 3 pounds of peppers. Round to the nearest hundredth.

Step-by-Step Solution

Answer

The total cost is \(\text{\textdollar} 6.72\).

Step 1: Determine the Discount Amount

Calculate the amount of discount that 25% represents. Multiply the original price by 0.25: \[ \text{Discount} = 2.99 \times 0.25 \]

Step 2: Calculate Discount Value

Perform the multiplication to find the discount value: \[ \text{Discount} = 2.99 \times 0.25 = 0.7475 \] Round to the nearest hundredth: \[ \text{Discount} \text{ (rounded)} = 0.75 \]

Step 3: Subtract Discount from Original Price

Subtract the discount from the original price to get the sale price: \[ \text{Sale Price} = 2.99 - 0.75 = 2.24 \]

Step 4: Find the Total Cost for 3 Pounds

Multiply the sale price by the number of pounds to find the total cost: \[ \text{Total Cost} = 2.24 \times 3 \]

Step 5: Calculate Total Cost

Perform the multiplication to find the total cost: \[ \text{Total Cost} = 2.24 \times 3 = 6.72 \]

Key Concepts

Percentage Calculation

Percentages represent a fraction of 100 and are a crucial part of many calculations. In our example, the bell peppers are on sale at 25% off. This means you save 25% of the original price. To determine the discount amount, we convert the percentage to a decimal by dividing by 100. So, 25% becomes 0.25. Then, we multiply the original price by this decimal. For the bell peppers costing \(2.99\) per pound, the discount calculation is: \(2.99 \times 0.25\). This gives us the discount amount before rounding.

Rounding Numbers

Rounding means adjusting a number to be closer to a given value. In our case, we round to the nearest hundredth, which is the second digit after the decimal point. After calculating the discount, we get \(0.7475\). To round \(0.7475\) to the nearest hundredth, we look at the thousandth place. Since \(7\) is greater than \(5\), we round up the hundredth place. Therefore, \(0.7475\) is rounded to \(0.75\). Rounding makes numbers easier to work with in practical situations.

Multiplication

Multiplication is one of the basic arithmetic operations and is repeatedly used in various calculations. After finding the discount, we subtract it from the original price to find the sale price: \(2.99 - 0.75 = 2.24\). Next, to find the cost for 3 pounds of peppers on sale, we multiply the sale price per pound by the number of pounds: \(2.24 \times 3\). This calculation is straightforward and gives us the total cost of \(6.72\). Multiplication helps in scaling values up, which is essential for finding totals.