Problem 35 - Prealgebra

Question

Omar bought a pair of shoes for \(20 \%\) off the original price and another \(25 \%\) off the discounted price. If the shoes originally cost \(\$ 45.50\), what was the final sale price?

Step-by-Step Solution

Answer

The final sale price of the shoes was $27.30.

Step 1: Calculate First Discount

To find the price after the 20% discount, we first determine 20% of the original price. The original price of the shoes is $45.50. Therefore, the first discount is calculated as follows:\[ \text{First Discount} = 0.20 \times 45.50 = 9.10 \]Subtract this discount from the original price to find the new price:\[ \text{Price after first discount} = 45.50 - 9.10 = 36.40 \]

Step 2: Calculate Second Discount

Next, apply the second discount of 25% to the already discounted price of \(36.40. Calculate 25% of \)36.40:\[ \text{Second Discount} = 0.25 \times 36.40 = 9.10 \]Subtract this second discount from the price after the first discount:\[ \text{Final Sale Price} = 36.40 - 9.10 = 27.30 \]

Step 3: Verify the Calculations

Recheck each step to ensure accuracy. We first found 20% of the original price and subtracted it to find the new price. Then, we calculated 25% of the new price to determine the final price. Each calculation appears correct.

Key Concepts

Step-by-Step Math Solutions

To tackle problems like the one Omar faced buying shoes, it's crucial to understand step-by-step math solutions. This approach systematically breaks down complex problems into smaller, more manageable steps. By doing this, students can follow along logically and ensure they fully understand each part of the solution.
This methodical process often involves writing out each step clearly and carrying forward intermediate results to the next calculation. This way,
it lessens the chance of error and allows for easy backtracking if something seems off.

• Identify what you need to find. In our example, it was the final sale price after sequential discounts.
• Calculate each required percentage or portion from the given data meticulously.
• Use intermediate results to proceed to the next calculation step by step.

By employing step-by-step solutions, you develop a habit of checking your work as you progress, leading to more accurate results.

Prealgebra Problem Solving

Prealgebra problem solving delivers the foundational tools needed for solving a variety of mathematical questions, such as calculating discounts. It focuses on understanding basic arithmetic operations and their properties, which are crucial when dealing with problems involving percentages.
When you receive an exercise like calculating a discount, approach it with the following mindset:

• Start by identifying the arithmetic operations needed (e.g., multiplication for percentages, subtraction for finding new prices).
• Consider the order of operations. For instance, apply one discount before the next!
• Make sure you fully understand the decimal conversion of percentages - for 20%, you'd use 0.20.

This step involves a lot of practice and patience, but with diligence, solving prealgebra problems becomes an intuitive and rewarding process.

Mathematical Calculations

Mathematical calculations are at the heart of solving percentage discount problems. They involve using arithmetic operations such as multiplication and subtraction, which are foundational in mathematics.
To solve the example problem, you need to grasp these core concepts:

• Multiplying percentages as decimals. Convert a percentage to a decimal by dividing by 100. For example, 20% becomes 0.20.
• Subtracting to find the new price. Always subtract the discount from the original or interim prices.
• Cascading discounts mean each discount is applied to the new price after the previous discount is taken off, not the original price.

By putting these mathematical concepts into practice, you'll efficiently handle calculations and solve complex problems with ease.