1. **Problem Statement:** We need to find Chris's earnings based on a tiered commission structure for different sales amounts (Q3). 2. **Formula and Rules:** Chris earns: - 6% on the first $20,000 - 2% on the next $80,000 - 0.8% on any amount above $100,000 We calculate earnings by applying these rates to the respective portions of the sales. 3. **Calculations for Q3:** (i) $75,000 sales: - First $20,000: $20,000 \times 0.06 = 1200$ - Remaining $55,000 (75,000 - 20,000): $55,000 \times 0.02 = 1100$ - Total: $1200 + 1100 = 2300$ (ii) $97,000 sales: - First $20,000: $20,000 \times 0.06 = 1200$ - Next $77,000 (97,000 - 20,000): $77,000 \times 0.02 = 1540$ - Total: $1200 + 1540 = 2740$ (iii) $112,500 sales: - First $20,000: $20,000 \times 0.06 = 1200$ - Next $80,000: $80,000 \times 0.02 = 1600$ - Remaining $12,500 (112,500 - 100,000): $12,500 \times 0.008 = 100$ - Total: $1200 + 1600 + 100 = 2900$ (iv) $185,000 sales: - First $20,000: $20,000 \times 0.06 = 1200$ - Next $80,000: $80,000 \times 0.02 = 1600$ - Remaining $85,000 (185,000 - 100,000): $85,000 \times 0.008 = 680$ - Total: $1200 + 1600 + 680 = 3480$ (v) $255,000 sales: - First $20,000: $20,000 \times 0.06 = 1200$ - Next $80,000: $80,000 \times 0.02 = 1600$ - Remaining $155,000 (255,000 - 100,000): $155,000 \times 0.008 = 1240$ - Total: $1200 + 1600 + 1240 = 4040$ --- 4. **Problem Statement:** Find Alf's earnings with a retainer and tiered commission for different sales amounts (Q4). 5. **Formula and Rules:** Alf earns: - Retainer: $240 per week - 2% on first $30,000 - 1.5% on next $80,000 - 0.8% on remainder Calculate earnings by summing retainer and commissions on each tier. 6. **Calculations for Q4:** (i) $98,000 sales: - Retainer: 240 - First $30,000: $30,000 \times 0.02 = 600$ - Next $68,000 (98,000 - 30,000): $68,000 \times 0.015 = 1020$ - Total: $240 + 600 + 1020 = 1860$ (ii) $135,000 sales: - Retainer: 240 - First $30,000: $30,000 \times 0.02 = 600$ - Next $80,000: $80,000 \times 0.015 = 1200$ - Remaining $25,000 (135,000 - 110,000): $25,000 \times 0.008 = 200$ - Total: $240 + 600 + 1200 + 200 = 2240$ (iii) $150,000 sales: - Retainer: 240 - First $30,000: $30,000 \times 0.02 = 600$ - Next $80,000: $80,000 \times 0.015 = 1200$ - Remaining $40,000 (150,000 - 110,000): $40,000 \times 0.008 = 320$ - Total: $240 + 600 + 1200 + 320 = 2360$ (iv) $200,000 sales: - Retainer: 240 - First $30,000: $30,000 \times 0.02 = 600$ - Next $80,000: $80,000 \times 0.015 = 1200$ - Remaining $90,000 (200,000 - 110,000): $90,000 \times 0.008 = 720$ - Total: $240 + 600 + 1200 + 720 = 2760$ (v) $175,000 sales: - Retainer: 240 - First $30,000: $30,000 \times 0.02 = 600$ - Next $80,000: $80,000 \times 0.015 = 1200$ - Remaining $65,000 (175,000 - 110,000): $65,000 \times 0.008 = 520$ - Total: $240 + 600 + 1200 + 520 = 2560$ --- 7. **Problem Statement:** Ian's income is $895 when he sells $40,000 worth of goods with a 0.5% commission. Find his retainer (Q5). 8. **Formula and Rules:** Income = Retainer + Commission Commission = 0.5% of sales = $40,000 \times 0.005 = 200$ 9. **Calculation:** $$895 = Retainer + 200$$ Subtract 200 from both sides: $$895 - \cancel{200} = Retainer + \cancel{200}$$ $$695 = Retainer$$ **Answer:** Ian's retainer is $695.