1. **State the problem:** We have three mothers with different incomes and a rebate system for before and after school care costing $10,000 per year. We want to find who has the least money left after paying for care. 2. **Define the rebate rules:** - Income $\leq 30000$: rebate 75% + $6000 school bonus. - Income $30000 < x \leq 40000$: rebate 55%, no bonus. - Income $> 40000$: rebate 30%, no bonus. 3. **Calculate rebate and leftover money for each mother:** **Jade:** earns $40001 > 40000$ - Rebate = 30% of $10000 = $3000 - No bonus - Cost after rebate = $10000 - $3000 = $7000 - Money left = $40001 - $7000 = $33001 **Emily:** earns $38000$ with $30000 < 38000 \leq 40000$ - Rebate = 55% of $10000 = $5500 - No bonus - Cost after rebate = $10000 - $5500 = $4500 - Money left = $38000 - $4500 = $33500 **Lucy:** earns $29550 \leq 30000$ - Rebate = 75% of $10000 = $7500 - Bonus = $6000 - Total rebate = $7500 + $6000 = $13500 (but rebate cannot exceed cost, so max rebate is $10000) - Cost after rebate = $10000 - $10000 = $0 - Money left = $29550 - $0 = $29550 4. **Compare leftover money:** - Jade: $33001$ - Emily: $33500$ - Lucy: $29550$ 5. **Conclusion:** Lucy has the least amount of money left after paying for before and after school care. **Final answer:** $29550$ is the least amount of money left after paying for care.