Objective 2 Solve using the five "Steps for Solving Applied...

Objective 2
Solve using the five "Steps for Solving Applied Problems." See Example 2
Katrina paid $\$ 20.40$ for a backpack that was marked down $15 \% .$ Find the original retail price of the backpack.

Key Concepts

Applied Problem-Solving Process

This is a structured method for solving complex problems, often broken down into several steps: understanding the problem, devising a plan, carrying out the plan, checking the solution, and reflecting on the process. It provides a clear strategy for translating a real-world scenario into mathematical equations and ensuring that the solution is reasonable and accurate.

Percentage Discounts

A percentage discount shows how much an item’s original price is reduced; it is calculated by taking a certain percentage off the original value. Understanding that a discount reduces the price to a certain remaining percentage (for example, a 15% discount means paying 85% of the original price) is key when solving problems related to sales and pricing.

Conversion of Percentages to Decimals

Converting percentages to decimals is essential for mathematical operations. This transformation, such as turning 15% into 0.15, allows for easy multiplication and subtraction, which are necessary steps in computing the remaining proportion of an original price after a percentage discount is applied.

Algebraic Equation Solving

This involves setting up an equation to represent the problem by defining a variable for the unknown quantity and applying algebraic manipulations to solve for it. It is a fundamental concept in mathematics that enables one to translate a real-world scenario, like calculating an original price after a discount, into a solvable mathematical expression.

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