1. **State the problem:** Nadia earns a weekly allowance of $400 plus 5% commission on her sales. We want to find: a) The total sales value when she earned $510.30. b) The average sales value when her average earnings are $780. 2. **Formula:** Total earnings = Base pay + Commission $$E = 400 + 0.05S$$ where $E$ is earnings and $S$ is total sales. 3. **Part (a): Find $S$ when $E = 510.30$** $$510.30 = 400 + 0.05S$$ Subtract 400 from both sides: $$510.30 - 400 = 0.05S$$ $$110.30 = 0.05S$$ Divide both sides by 0.05: $$\frac{110.30}{\cancel{0.05}} = \frac{0.05S}{\cancel{0.05}}$$ $$S = 2206$$ 4. **Part (b): Find $S$ when $E = 780$** $$780 = 400 + 0.05S$$ Subtract 400: $$780 - 400 = 0.05S$$ $$380 = 0.05S$$ Divide both sides by 0.05: $$\frac{380}{\cancel{0.05}} = \frac{0.05S}{\cancel{0.05}}$$ $$S = 7600$$ **Final answers:** - (a) Total sales = $2206$ - (b) Average weekly sales = $7600$