Objectives 2 and 3 Mixed Exercises Solve using the five...

Objectives 2 and 3 Mixed Exercises Solve using the five "Steps for Solving Applied Problems." In Johnson County, 8330 people were collecting unemployment benefits in September 2006 . This is $2 \%$ less than the number collecting the benefits in September $2005 .$ How many people in Johnson County were getting unemployment benefits in September $2005 ?$

Objectives 2 and 3 Mixed Exercises
Solve using the five "Steps for Solving Applied Problems."
In Johnson County, 8330 people were collecting unemployment benefits in September 2006 . This is $2 \%$ less than the number collecting the benefits in September $2005 .$ How many people in Johnson County were getting unemployment benefits in September $2005 ?$

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Key Concepts

Percentage Decrease

This concept involves understanding that when a quantity decreases by a certain percent, the new value represents a fraction of the original. For example, a 2% decrease means the current amount is 98% of the initial value, which is crucial when determining the original number after a reduction.

Reverse Calculation of Percentages

This concept refers to finding an original value when given a result that has been altered by a percentage change. In cases of a decrease, it involves dividing the known reduced amount by the remaining percentage (expressed as a decimal), effectively 'undoing' the percentage change.

Translating Word Problems into Equations

This key concept emphasizes the skill of reading a real-world scenario and converting it into a mathematical equation. It involves identifying the known quantities, the unknown variable, and the relationship between them, which is essential for setting up an equation that reflects the problem context.

Algebraic Equation Solving

Once the problem is modeled by an equation, solving it requires using algebraic techniques to isolate the unknown variable. This includes applying inverse operations and manipulation of the equation, which is a fundamental strategy in algebra for finding solutions to applied problems.

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