Multi-step problems with percents

Learning Objectives Identify the sequence of operations required to solve multi-step percent problems. Calculate discounts, sales tax, and tips on an original price. Determine the final price of an item after applying multiple percentage changes (e.g., discount then tax). Calculate commissions and total earnings involving a base salary and a percentage of sales. Solve problems involving successive percentage changes, understanding that they are applied to the new amount. Work backward to find an original price given a final price after multiple percentage changes. Apply their understanding of multi-step percent problems to real-world consumer scenarios. Ever wondered how stores calculate the final price of a sale item after adding tax? 🛍️ Or how much you should tip on a re...

TermDefinitionExample PercentA ratio that compares a number to 100. It represents 'parts per hundred'.25% means 25 out of 100, or 0.25 as a decimal. DiscountA reduction in the original price of an item, usually expressed as a percentage.A shirt originally priced at $40 with a 20% discount means you save $8. Sales TaxA percentage of the selling price of goods or services that is added to the cost and collected by the government.If a $10 item has a 7% sales tax, you pay an additional $0.70. Tip (Gratuity)An amount of money paid to someone for a service, typically calculated as a percentage of the service cost.Leaving a 15% tip on a $50 meal means adding $7.50 to the bill. CommissionA fee paid to an employee for making a sale, usually a percentage of the sale price.A salesperson ea...

Calculating a Percentage of a Number $\text{Part} = \text{Percent (as decimal)} \times \text{Whole}$ To find a certain percentage of a given number, convert the percentage to a decimal (divide by 100) and then multiply it by the whole number. This is used for calculating discounts, taxes, tips, or commissions. Calculating New Amount After a Percent Increase $\text{New Amount} = \text{Original Amount} \times (1 + \text{Percent Increase (as decimal)})$ Use this rule when an amount is increasing by a percentage, such as adding sales tax or a tip. The '1' represents 100% of the original amount. Calculating New Amount After a Percent Decrease $\text{New Amount} = \text{Original Amount} \times (1 - \text{Percent Decrease (as decimal)})$ Use this rule when an amou...