- Problem 6: The thought number is x. The equation is x/5 - 154 = 6. Solving for x: x/5 = 160, so x = 800.
- Problem 7: Let the lorry's speed be x km/h, then the car's speed is (x + 5) km/h. They meet after 4 hours, covering a total distance of 380 km. The equation is 4(x + 5) + 4x = 380. Simplifying: 4x + 20 + 4x = 380, so 8x = 360, and x = 45. Therefore, the lorry's speed is 45 km/h and the car's speed is 50 km/h.
- Problem 8: Let one side of the rectangle be x cm (x > 3), then the other side is (x - 3) cm. The original area is S₁ = x(x - 3). After increasing each side by 1 cm, the new sides are (x + 1) cm and (x - 2) cm, and the new area is S₂ = (x + 1)(x - 2). The area increases by 18 cm², so S₁ + 18 = S₂. This gives x(x - 3) + 18 = (x + 1)(x - 2). Expanding: x² - 3x + 18 = x² - x - 2. Simplifying: -3x + 18 = -x - 2, so -2x = -20, and x = 10. The sides are 10 cm and 7 cm.
- Problem 9: Let the first cow's yield in the first year be x liters, then the second cow's yield is (8100 - x) liters. In the second year, the first cow's yield is 1.15x and the second cow's yield is 1.10(8100 - x). The total second-year yield is 9100 liters, so 1.15x + 1.10(8100 - x) = 9100. Expanding: 1.15x + 8910 - 1.10x = 9100. Simplifying: 0.05x = 190, so x = 3800. The first cow yielded 3800 liters in the first year and 4370 liters in the second year. The second cow yielded 4300 liters in the first year and 4730 liters in the second year.
Parent Tip: Review the logic above to help your child master the concept of quadratic equation word problems worksheet with answers.
