Confidential information - This is for official consumption $$ \begin{array}{l} ext { I use } \frac{1}{12} ext { of my salary to pay for rates and taxes, } \frac{1}{16} ext { to pay for insurance and } \frac{5}{6} \ ext { to meet other expenses. If I have R320 left of my monthly salary, calculate my } \ ext { yearly salary. }\end{array} $$

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Confidential information - This is for official consumption $$ \begin{array}{l}	ext { I use } \frac{1}{12} 	ext { of my salary to pay for rates and taxes, } \frac{1}{16} 	ext { to pay for insurance and } \frac{5}{6} \ 	ext { to meet other expenses. If I have R320 left of my monthly salary, calculate my } \ 	ext { yearly salary. }\end{array} $$

UpStudy AI · Accepted Answer

To solve this problem, we need to first calculate the total amount of money spent on rates and taxes, insurance, and other expenses.

Let's denote the monthly salary as $$ M $$.

Given:
- $$ \frac{1}{12} $$ of the salary is spent on rates and taxes.
- $$ \frac{1}{16} $$ of the salary is spent on insurance.
- $$ \frac{5}{6} $$ of the salary is spent on other expenses.

We know that the total amount spent on all expenses is equal to the monthly salary minus the amount left over ($$ R320 $$).

Let's set up the equation to represent the total amount spent on all expenses:
$$ \frac{1}{12}M + \frac{1}{16}M + \frac{5}{6}M = M - 320 $$

Now, we can solve this equation to find the monthly salary $$ M $$, and then calculate the yearly salary by multiplying the monthly salary by 12.
Solve the equation by following steps:
- step0: Solve for $$M$$:
  $$\frac{1}{12}M+\frac{1}{16}M+\frac{5}{6}M=M-320$$
- step1: Add the terms:
  $$\frac{47}{48}M=M-320$$
- step2: Move the variable to the left side:
  $$\frac{47}{48}M-M=-320$$
- step3: Subtract the terms:
  $$-\frac{1}{48}M=-320$$
- step4: Change the signs:
  $$\frac{1}{48}M=320$$
- step5: Multiply by the reciprocal:
  $$\frac{1}{48}M\times 48=320\times 48$$
- step6: Multiply:
  $$M=15360$$
The solution to the equation is $$ M = 15360 $$, which represents the monthly salary.

Now, to find the yearly salary, we multiply the monthly salary by 12:
$$ \text{Yearly Salary} = 15360 \times 12 = 184320 $$

Therefore, the yearly salary is R184,320.
The yearly salary is R184,320.

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