Question

Kim bought a pair of shoes on sale for $\$ 40.50 .$ The sale price was 45$\%$ of the original price. What was the original price of the shoes?

   Kim bought a pair of shoes on sale for $\$ 40.50 .$ The sale price was 45$\%$ of the original price. What was the original price of the shoes?
 
Prealgebra
Prealgebra
Lynn Marecek,… 1st Edition
Chapter 9, Problem 14 ↓

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We can represent this as a proportion, where the sale price is the part and the original price is the whole. So, we have $\frac{45}{100} = \frac{40.50}{x}$, where x is the original price.  Show more…

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Kim bought a pair of shoes on sale for $\$ 40.50 .$ The sale price was 45$\%$ of the original price. What was the original price of the shoes?
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Key Concepts

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Solving Linear Equations
Solving linear equations involves isolating the unknown variable to determine its value. This method is essential in problems where a percentage of an unknown quantity is given, allowing for the determination of the original or complete value through inverse operations.
Algebraic Equation Setup
Setting up an algebraic equation is crucial in translating word problems into solvable mathematical expressions. In percentage problems, this often involves representing the relationship between the known part and the unknown whole using the decimal equivalent of the percentage.
Percentage
Percentage is a way of expressing a number as a fraction of 100. It is a fundamental concept in math that helps compare parts to a whole and is widely used in various calculations including discounts, interest rates, and statistical data.
Converting Percentages to Decimals
Converting a percentage to a decimal simplifies the process of solving equations involving percentages. This conversion is done by dividing the percentage by 100, which allows for direct multiplication with other numbers in algebraic calculations.

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