Anna saved 1950, which was 65 % of the amount she needed for a used car. What was the total amo

step 1 So we have 1950 is 60 % of what total? So we have 1950 is equal to x times 0 .65. We're going to

Anna saved 1950, which was 65 % of the amount she needed...

Key Concepts

Percentage

A percentage represents a part out of a hundred and is a way to express proportions. In problems involving percentages, a specified percentage of a total quantity is often equated to a known value, which then allows for the determination of the unknown quantity. This concept is fundamental in comparing parts to a whole in various contexts.

Decimal Conversion

Decimal conversion involves converting a percentage into its decimal form to simplify arithmetic operations. For instance, converting 65% to 0.65 makes it easier to set up equations and perform calculations like multiplication or division. This step is essential as it bridges the gap between percent notation and numerical computation.

Linear Equations

Linear equations are mathematical statements that involve a constant rate of change, typically represented in the form ax = b. In the context of percentage problems, setting up a linear equation involves equating the known percentage (in decimal form) of an unknown total to a given value, then solving for that total. This method is widely applicable in algebra and real-life problems.

Proportional Reasoning

Proportional reasoning is the ability to understand and manipulate ratios and proportions. When one quantity is a specified percentage of another, a proportional relationship exists between them. Identifying and using this relationship allows for the scaling of one value to find another, which is critical in solving problems where one part of a total is known.

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