1. **Stating the problem:** We have a price that undergoes a series of percentage changes: an increase of 20%, a decrease of 10%, an increase twice of 5%, and a one-time increase of 10%. We want to find the overall percentage change after all these adjustments. 2. **Formula and rules:** To apply percentage changes sequentially, convert each percentage to a multiplier: an increase of $p\%$ corresponds to multiplying by $1 + \frac{p}{100}$, and a decrease of $p\%$ corresponds to multiplying by $1 - \frac{p}{100}$. 3. **Calculate each multiplier:** - Increase 20%: multiplier = $1 + \frac{20}{100} = 1.20$ - Decrease 10%: multiplier = $1 - \frac{10}{100} = 0.90$ - Increase twice of 5% means two increases of 5%, so multiply by $1.05$ twice. - One-time increase of 10%: multiplier = $1 + \frac{10}{100} = 1.10$ 4. **Combine all multipliers:** $$ \text{Total multiplier} = 1.20 \times 0.90 \times 1.05 \times 1.05 \times 1.10 $$ 5. **Calculate step-by-step:** $$ 1.20 \times 0.90 = 1.08 $$ $$ 1.08 \times 1.05 = 1.134 $$ $$ 1.134 \times 1.05 = 1.1907 $$ $$ 1.1907 \times 1.10 = 1.30977 $$ 6. **Interpretation:** The total multiplier is approximately $1.30977$, which means the price increased by about $30.977\%$ overall. 7. **Final answer:** The overall percentage change after all adjustments is approximately **30.98% increase**.