Subjects algebra

Salary Calculation Aa1B06

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1. **State the problem:** Antony spends parts of his net salary on various expenses and ends up with 15800. We need to find his original salary. 2. **Define variables:** Let Antony's net salary be $S$. 3. **Calculate school fees:** He spends one-quarter on school fees, so amount spent is $\frac{1}{4}S$. 4. **Remaining after school fees:** $S - \frac{1}{4}S = \frac{3}{4}S$. 5. **Calculate bills:** He spends 25% (which is $\frac{1}{4}$) of the remaining on bills, so bills = $\frac{1}{4} \times \frac{3}{4}S = \frac{3}{16}S$. 6. **Remaining after bills:** $\frac{3}{4}S - \frac{3}{16}S = \frac{12}{16}S - \frac{3}{16}S = \frac{9}{16}S$. 7. **Calculate transport:** He spends one-ninth of what was left on transport, so transport = $\frac{1}{9} \times \frac{9}{16}S = \frac{1}{16}S$. 8. **Remaining after transport:** $\frac{9}{16}S - \frac{1}{16}S = \frac{8}{16}S = \frac{1}{2}S$. 9. **Final amount:** Given as 15800, so $\frac{1}{2}S = 15800$. 10. **Solve for $S$:** $$ \frac{1}{2}S = 15800 $$ Multiply both sides by 2: $$ \cancel{\frac{1}{2}} \times 2 S = 15800 \times 2 $$ $$ S = 31600 $$ **Answer:** Antony's net salary is 31600.