1. **Problem statement:** Majid pays a total of 51520 for his car insurance, which includes a basic charge plus 15% sales tax. We need to find the amount of sales tax Majid pays. 2. **Formula and explanation:** Let the basic charge be $B$. The sales tax is 15% of $B$, so sales tax = $0.15B$. The total amount paid is the sum of the basic charge and sales tax: $$\text{Total} = B + 0.15B = 1.15B$$ 3. **Calculate the basic charge:** $$1.15B = 51520$$ $$B = \frac{51520}{1.15} = 44800$$ 4. **Calculate the sales tax:** $$\text{Sales tax} = 0.15 \times 44800 = 6720$$ --- 1. **Problem statement:** A campsite is a rectangle with sides $(3x + 6)$ m and $(x + 1)$ m, and the diagonal length is $(4x + 1)$ m. Find the area and perimeter. 2. **Formula and explanation:** For a rectangle with sides $a$ and $b$, the diagonal $d$ satisfies the Pythagorean theorem: $$d^2 = a^2 + b^2$$ The area is: $$\text{Area} = a \times b$$ The perimeter is: $$\text{Perimeter} = 2(a + b)$$ 3. **Apply the Pythagorean theorem:** $$ (4x + 1)^2 = (3x + 6)^2 + (x + 1)^2 $$ Expand each term: $$ (4x + 1)^2 = 16x^2 + 8x + 1 $$ $$ (3x + 6)^2 = 9x^2 + 36x + 36 $$ $$ (x + 1)^2 = x^2 + 2x + 1 $$ 4. **Set up the equation:** $$16x^2 + 8x + 1 = 9x^2 + 36x + 36 + x^2 + 2x + 1$$ Simplify the right side: $$16x^2 + 8x + 1 = 10x^2 + 38x + 37$$ 5. **Bring all terms to one side:** $$16x^2 + 8x + 1 - 10x^2 - 38x - 37 = 0$$ $$6x^2 - 30x - 36 = 0$$ 6. **Simplify by dividing by 6:** $$x^2 - 5x - 6 = 0$$ 7. **Solve quadratic equation:** $$x = \frac{5 \pm \sqrt{(-5)^2 - 4 \times 1 \times (-6)}}{2} = \frac{5 \pm \sqrt{25 + 24}}{2} = \frac{5 \pm \sqrt{49}}{2}$$ $$x = \frac{5 \pm 7}{2}$$ 8. **Possible values:** $$x = \frac{5 + 7}{2} = 6$$ $$x = \frac{5 - 7}{2} = -1$$ Since length cannot be negative, $x = 6$. 9. **Calculate sides:** $$a = 3x + 6 = 3(6) + 6 = 18 + 6 = 24$$ $$b = x + 1 = 6 + 1 = 7$$ 10. **Calculate area:** $$\text{Area} = 24 \times 7 = 168$$ 11. **Calculate perimeter:** $$\text{Perimeter} = 2(24 + 7) = 2 \times 31 = 62$$ **Final answers:** - Sales tax Majid pays: 6720 - Campsite area: 168 m² - Campsite perimeter: 62 m