I use \( \frac{1}{12} \) of my salary to pay for rates and taxes, \( \frac{1}{16} \) to pay for insurance and \( \frac{5}{6} \) to meet other expenses. If I have R320 left of my monthly salary, calculate my yearly salary.

To solve for your yearly salary, let's first set your monthly salary as \( S \). According to the proportions of your salary: 1. Rates and taxes: \( \frac{1}{12}S \) 2. Insurance: \( \frac{1}{16}S \) 3. Other expenses: \( \frac{5}{6}S \) The sum of these expenses plus the R320 you have left must equal your salary: \[ \frac{1}{12}S + \frac{1}{16}S + \frac{5}{6}S + 320 = S \] To simplify calculations, let's find a common denominator for \( \frac{1}{12} \), \( \frac{1}{16} \), and \( \frac{5}{6} \). The least common multiple of 12, 16, and 6 is 48. Rewriting each fraction: - \( \frac{1}{12}S = \frac{4}{48}S \) - \( \frac{1}{16}S = \frac{3}{48}S \) - \( \frac{5}{6}S = \frac{40}{48}S \) Now substitute back into the equation: \[ \frac{4}{48}S + \frac{3}{48}S + \frac{40}{48}S + 320 = S \] Combine like terms: \[ \frac{47}{48}S + 320 = S \] Now, move \( \frac{47}{48}S \) to the other side of the equation: \[ 320 = S - \frac{47}{48}S \] This simplifies to: \[ 320 = \frac{1}{48}S \] Multiply both sides by 48 to isolate \( S \): \[ S = 320 \times 48 \] \[ S = 15360 \] Your monthly salary is R15,360. To find the yearly salary, multiply by 12: \[ Yearly Salary = 15360 \times 12 = 184320 \] So, your yearly salary is R184,320.