1. **State the problem:** Ken earns $8 per hour for the first 10 hours and $10 per hour for the remaining hours. He saves 90% of his total earnings and wants to save at least 270. We need to find the minimum number of hours he must work after the first 10 hours. 2. **Define variables:** Let $h$ be the number of hours worked after the first 10 hours. 3. **Calculate earnings:** - Earnings for first 10 hours: $8 \times 10 = 80$ - Earnings for remaining $h$ hours: $10 \times h = 10h$ - Total earnings: $80 + 10h$ 4. **Savings condition:** Ken saves 90% of his earnings, so savings are $0.9 \times (80 + 10h)$. 5. **Set up inequality:** Savings must be at least 270, so $$0.9 \times (80 + 10h) \geq 270$$ 6. **Solve inequality:** $$0.9 \times (80 + 10h) \geq 270$$ $$72 + 9h \geq 270$$ $$9h \geq 270 - 72$$ $$9h \geq 198$$ $$h \geq \frac{198}{9} = 22$$ 7. **Interpretation:** Ken must work at least 22 hours after the first 10 hours to save at least 270. **Final answer:** $\boxed{22}$ hours