Subjects algebra

Salary Savings

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Salary Savings


1. **State the problem:** Calculate the annual salary at the end of the 3rd year given a starting salary and raises every 6 months. 2. **Step 1:** Identify the starting salary: Birr 25,250 per year. 3. **Step 2:** The raise amount is Birr 250 every 6 months, so 2 raises per year. 4. **Step 3:** Calculate number of 6-month periods in 3 years: $$3 \text{ years} \times 2 = 6$$ raises. 5. **Step 4:** Calculate total raise after 3 years: $$6 \times 250 = 1500$$ Birr. 6. **Step 5:** Add total raise to starting salary: $$25,250 + 1500 = 26,750$$ Birr. --- 7. **State the problem:** Find the amount Bontu will save in the 8th year if she saves 1000 in the first year and increases savings by 200 each subsequent year. 8. **Step 1:** Define the pattern: savings increase by 200 each year, so the savings in year $$n$$ is arithmetic sequence: $$a_n = a_1 + (n-1)d$$ 9. **Step 2:** Substitute given values: $$a_1 = 1000$$, $$d = 200$$, $$n = 8$$ 10. **Step 3:** Calculate savings in 8th year: $$a_8 = 1000 + (8-1) \times 200 = 1000 + 7 \times 200 = 1000 + 1400 = 2400$$ Birr. **Final answers:** - Annual salary at the end of the 3rd year: Birr 26,750. - Amount saved by Bontu during the 8th year: Birr 2,400.