SAT-Style: Multi-Step Percentage Problems

SAT Math · Axiom Academy

SAT-Style Multi-Step Percentage Problems Worked example: Markups, discounts, and compound percentages Problem 1: Markup Then Discount A retailer buys jackets at a cost of 40 each. The store marks up the price by 50%, then during a sale, offers a 25% discount on the marked-up price. What is the final selling price of the jacket? Step 1: Understand What We're Looking For We need to find the final price after two sequential percentage changes. The key is that each change applies to the result of the previous step, not the original cost. Step 2: Calculate the Marked-Up Price The retailer marks up the price by 50% of the original 40. Step 3: Calculate the Final Price After Discount During the sale, the store discounts the marked-up price of 60 by 25%. The final selling price is 45. Problem 2: Finding the Overall Percent Change A population of 1,000 fish increases by 20% in the first year, then decreases by 15% in the second year. What is the overall percent change over the two years? (Express as a percent increase or decrease.) Step 1: Calculate Population After Year 1 A 20% increase means we multiply by 1.20. Step 2: Calculate Population After Year 2 A 15% decrease means we multiply by 0.85. Note: The decrease is applied to the new population of 1200, not the original 1000. Step 3: Calculate Overall Percent Change Compare the final population to the original. The population increased by 2% overall. Problem 3: Working Backward from Percent Change

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