1. **Stating the problem:** We have a laptop shop selling two types of laptops: budget and premium. The total number of laptops sold in one day is 50. Budget laptops cost 20000 each, premium laptops cost 50000 each. Total revenue earned is 1700000. We need to find how many budget and premium laptops were sold. 2. **Forming the equations:** Let $x$ = number of budget laptops, $y$ = number of premium laptops. From the problem: - Total laptops sold: $$x + y = 50$$ - Total revenue: $$20000x + 50000y = 1700000$$ 3. **Solving the system:** From the first equation: $$y = 50 - x$$ Substitute into the second equation: $$20000x + 50000(50 - x) = 1700000$$ Simplify: $$20000x + 2500000 - 50000x = 1700000$$ Combine like terms: $$\cancel{20000x} - 50000x + 2500000 = 1700000$$ $$-30000x + 2500000 = 1700000$$ Subtract 2500000 from both sides: $$-30000x = 1700000 - 2500000$$ $$-30000x = -800000$$ Divide both sides by -30000: $$x = \frac{-800000}{-30000} = \cancel{\frac{-800000}{-30000}} = \frac{800000}{30000}$$ Simplify the fraction: $$x = \frac{800000 \div 10000}{30000 \div 10000} = \frac{80}{3} \approx 26.67$$ Since number of laptops must be whole numbers, check calculation again: Actually, simplify exactly: $$x = \frac{800000}{30000} = \frac{800000 \div 1000}{30000 \div 1000} = \frac{800}{30} = \frac{80}{3}$$ This is not an integer, so re-check the arithmetic. Recalculate: $$20000x + 50000(50 - x) = 1700000$$ $$20000x + 2500000 - 50000x = 1700000$$ $$-30000x + 2500000 = 1700000$$ $$-30000x = 1700000 - 2500000 = -800000$$ $$x = \frac{-800000}{-30000} = \frac{800000}{30000}$$ Divide numerator and denominator by 1000: $$x = \frac{800}{30} = \frac{80}{3} = 26.67$$ This suggests a decimal, but since laptops sold must be integers, the problem likely expects integer solution. Try solving by substitution or elimination: Multiply first equation by 20000: $$20000x + 20000y = 1000000$$ Subtract this from revenue equation: $$(20000x + 50000y) - (20000x + 20000y) = 1700000 - 1000000$$ $$30000y = 700000$$ $$y = \frac{700000}{30000} = \frac{700000 \div 1000}{30000 \div 1000} = \frac{700}{30} = \frac{70}{3} = 23.33$$ Again decimal. Since decimals appear, the problem might allow fractional laptops or rounding. 4. **Final answer:** Number of budget laptops sold: approximately 27 Number of premium laptops sold: approximately 23 **Summary:** - Equations: $$x + y = 50$$ $$20000x + 50000y = 1700000$$ - Solution: $$x \approx 27, y \approx 23$$