Multistep problems with percents

Learning Objectives Deconstruct complex word problems into a sequence of individual percent calculations. Accurately calculate the final value after applying consecutive percent increases and decreases. Solve real-world problems involving discounts, markups, and sales tax in multiple steps. Calculate the value of an investment after earning interest and paying a percentage-based fee. Translate multistep percent scenarios into a single algebraic expression. Determine the original value when given the final value after several percentage changes have occurred. You see a $200 gaming headset with a 20% off sticker, but you also have a coupon for an additional 10% off. Is that the same as 30% off? Let's find out! 🛍️ This tutorial will guide you through solving problems that...

TermDefinitionExample Consecutive PercentsThe process of applying two or more percentage changes one after another. The key is that the base for each new percentage calculation is the result of the previous one.A stock worth $100 goes up 10% (to $110). It then drops 10%. The 10% drop is calculated from $110, not the original $100. Percent of a PercentA calculation where you find a percentage of a value that is already a percentage of another value.Finding what 50% of 20% is. This would be 0.50 * 0.20 = 0.10, or 10%. Base ValueThe 'whole' or original amount upon which a percentage is calculated. In multistep problems, this base value changes after each step.If an item is discounted, the original price is the first base. The discounted price then becomes the new base for calculati...

Sequential Calculation Multiplier Final Value = Original Value * (1 ± r₁) * (1 ± r₂) * ... Use this to chain multiple percent changes together. Use '+' for a percent increase (like tax or markup) and '-' for a percent decrease (like a discount). 'r' represents the percent rate as a decimal. Percent Change Percent Change = ((New Value - Original Value) / Original Value) * 100% Use this formula to find the total percent change after multiple steps have been completed. A positive result is a percent increase, and a negative result is a percent decrease. Simple Interest A = P(1 + rt) Calculates the total amount (A) in an account after 't' years with an initial principal (P) and an annual interest rate (r). This is less common in mu...