1. **Stating the problem:** We have the charge formula for a repair: $$C = \frac{20h + xh}{d}$$ where $C$ is the charge, $h$ is hours worked, $x$ is extra hourly charge, and $d$ is discount rate ($d \geq 1$). 2. **Part (i): Find $C$ when $h=3$, $x=3.5$, and $d=1.1$** 3. Substitute the values into the formula: $$C = \frac{20 \times 3 + 3.5 \times 3}{1.1}$$ 4. Calculate the numerator: $$20 \times 3 = 60$$ $$3.5 \times 3 = 10.5$$ So, $$C = \frac{60 + 10.5}{1.1} = \frac{70.5}{1.1}$$ 5. Simplify the fraction: $$C = \frac{\cancel{70.5}}{\cancel{1.1}} = 64.09$$ (rounded to 2 decimal places) 6. **Part (ii): Find $x$ when $C=76$, $h=4$, and $d=1.2$** 7. Start with the formula: $$76 = \frac{20 \times 4 + x \times 4}{1.2}$$ 8. Multiply both sides by $1.2$ to clear the denominator: $$76 \times 1.2 = 20 \times 4 + 4x$$ $$91.2 = 80 + 4x$$ 9. Subtract 80 from both sides: $$91.2 - 80 = 4x$$ $$11.2 = 4x$$ 10. Divide both sides by 4: $$\frac{11.2}{4} = x$$ $$x = 2.8$$ **Final answers:** (i) $C = 64.09$ (ii) $x = 2.8$