Subjects algebra

Percentage Changes 78Fd86

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1. **Stating the problem:** Calculate the sale price when the original price is 230 and the sale price is 92. 2. **Formula used:** The absolute change is calculated as $$\text{Absolute change} = \text{New value} - \text{Original value}$$ The percentage change is calculated as $$\text{Percentage change} = \frac{\text{Absolute change}}{\text{Original value}} \times 100\%$$ 3. **Calculate absolute change:** $$\text{Absolute change} = 92 - 230 = -138$$ 4. **Calculate percentage change:** $$\text{Percentage change} = \frac{-138}{230} \times 100\% = -60\%$$ 5. **Interpretation:** The sale price is a 60% decrease from the original price. --- **Next, complete the missing percentage changes in the table:** - For 75 to 40: - Absolute change: $$40 - 75 = -35$$ - Percentage change: $$\frac{-35}{75} \times 100\% = -46.7\%$$ (decrease) - For 36 to 100: - Absolute change: $$100 - 36 = 64$$ - Percentage change: $$\frac{64}{36} \times 100\% = 177.8\%$$ (increase) - For 43 to 12: - Absolute change: $$12 - 43 = -31$$ - Percentage change: $$\frac{-31}{43} \times 100\% = -72.1\%$$ (decrease) - For 90 to 234: - Absolute change: $$234 - 90 = 144$$ - Percentage change: $$\frac{144}{90} \times 100\% = 160\%$$ (increase) --- **Finally, solve the flowchart problem:** - Start with 600. - Increase by 40%: $$600 + 0.40 \times 600 = 600 + 240 = 840$$ - Decrease by 10%: $$840 - 0.10 \times 840 = 840 - 84 = 756$$ - Decrease by 50%: $$756 - 0.50 \times 756 = 756 - 378 = 378$$ **Final value after all changes is 378.**