During the nineteenth century, 75,029 new words entered the...

During the nineteenth century, $75,029$ new words entered the English language. This is about $46.9 \%$ more than the number of new words entered in the seventeenth century. (Source: Philip Durkin and Katherine Martin, Oxford University Press; "English by the Book," National Geographic, December 2013 ) Find the number of new words that appeared in the English language in the seventeenth century.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Algebraic Equations

Algebraic equations are used to express relationships between quantities and to solve for unknown values. In the context of percentage problems, setting up an equation such as final_value = original_value × (1 + rate) enables the determination of the original value when only the final value and the rate of increase are known.

Percentage Increase

This concept involves determining how much a quantity grows relative to its original value, expressed as a percentage. It is calculated by taking the difference between the new and original values, dividing by the original value, and often converting the result into a percentage format. It serves as a foundational tool for comparing relative changes over time.

Reverse Percentage Problem

A reverse percentage problem involves working backwards from a known value that has been increased (or decreased) by a certain percentage to find the original value. It requires setting up an equation where the final amount is represented as the original amount multiplied by a factor, typically (1 + the percentage increase expressed as a decimal), and then solving for the original amount.

Transcript

Please give Ace some feedback