Percent of change: word problems

Learning Objectives Identify the original and new amounts in a word problem. Calculate the amount of change (increase or decrease) from given values. Distinguish between percent increase and percent decrease scenarios. Apply the percent of change formula correctly to solve word problems. Interpret the calculated percent of change in the context of the word problem. Solve multi-step word problems involving percent of change. Ever wonder how stores calculate sale prices or how much a company's profits grew? 🤔 It's all about understanding percent of change! In this lesson, you'll learn how to tackle word problems that involve finding the percent of change. We'll explore how to calculate both percent increase and percent decrease, giving you essential skill...

TermDefinitionExample Original AmountThe starting value or initial quantity before any change occurs.If a shirt cost $20 yesterday and costs $15 today, $20 is the original amount. New AmountThe ending value or final quantity after a change has occurred.If a shirt cost $20 yesterday and costs $15 today, $15 is the new amount. Amount of ChangeThe absolute difference between the new amount and the original amount. It tells you how much the value has increased or decreased.If a price goes from $50 to $60, the amount of change is $60 - $50 = $10. Percent of ChangeA ratio that expresses the amount of change as a percentage of the original amount. It indicates the relative size of the change.If a price increased by $10 from an original of $50, the percent of change is ($10/$50) * 100% = 20%. Per...

Formula for Amount of Change $$ \text{Amount of Change} = |\text{New Amount} - \text{Original Amount}| $$ This formula calculates the absolute difference between the new and original amounts. The absolute value ensures the result is always positive, representing the magnitude of the change. Formula for Percent of Change $$ \text{Percent of Change} = \frac{\text{Amount of Change}}{\text{Original Amount}} \times 100\% $$ This is the primary formula to find the percent of change. First, calculate the amount of change, then divide it by the original amount, and finally multiply by 100% to express it as a percentage. Formula for Percent Increase $$ \text{Percent Increase} = \frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \times 100\% $$ Use this...