Subjects algebra

Pension Contributions 148850

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1. **Problem statement:** Martina's pension contributions follow a ratio of 3:3:1 for employee, employer, and government respectively, totaling 7 parts. Martina's total pension savings in the first year is 1351. We need to find how much each party contributed. 2. **Formula and explanation:** The total ratio parts are $3 + 3 + 1 = 7$. The total amount 1351 corresponds to these 7 parts. To find each contribution, divide 1351 by 7 to find the value of one part, then multiply by each ratio number. 3. **Calculations:** $$\text{Value of one part} = \frac{1351}{7} = 193\n$$ - Martina's contribution: $3 \times 193 = 579$ - Employer's contribution: $3 \times 193 = 579$ - Government's contribution: $1 \times 193 = 193$ 4. **Answer for (i):** - Martina: 579 - Employer: 579 - Government: 193 --- 5. **Problem statement (ii):** Brian contributes 731.25 as an employee, which is 1.5% of his gross income. Find his gross income. 6. **Formula:** Contribution = Gross Income $\times$ Contribution Rate 7. **Calculations:** $$731.25 = \text{Gross Income} \times 0.015$$ Divide both sides by 0.015: $$\text{Gross Income} = \frac{731.25}{0.015}$$ Show cancellation: $$\text{Gross Income} = \frac{731.25}{\cancel{0.015}} \times \frac{\cancel{1}}{1} = 48750$$ 8. **Answer for (ii):** Brian's gross income is 48750. **Final answers:** (i) Martina: 579, Employer: 579, Government: 193 (ii) Brian's gross income: 48750