Rachel's annual salary is $360,000. She spends 1/2 of her salary on rent, 1/8 on food, and 4/5 of the remaining amount in a bank. How much does she save every year?

Steps to Solve

1. Calculate Rent Expenses
   Rachel spends $\frac{1}{2}$ of her salary on rent.
   Her salary is $360,000. Therefore, her rent expenses are:
   $$ \text{Rent} = \frac{1}{2} \times 360000 = 180000 $$

2. Calculate Food Expenses
   Rachel spends $\frac{1}{8}$ of her salary on food.
   Thus, her food expenses are:
   $$ \text{Food} = \frac{1}{8} \times 360000 = 45000 $$

3. Calculate Transport Expenses
   Rachel spends $\frac{1}{12}$ of her salary on transport.
   Her transport expenses are calculated as:
   $$ \text{Transport} = \frac{1}{12} \times 360000 = 30000 $$

4. Calculate Total Expenses
   Now, add up all her expenses:
   $$ \text{Total Expenses} = \text{Rent} + \text{Food} + \text{Transport} $$
   Substituting the values:
   $$ \text{Total Expenses} = 180000 + 45000 + 30000 = 255000 $$

5. Calculate Remaining Amount After Expenses
   To find the remaining amount after her expenses: $$ \text{Remaining} = \text{Salary} - \text{Total Expenses} $$
   So,
   $$ \text{Remaining} = 360000 - 255000 = 105000 $$

6. Calculate Savings
   Rachel saves $\frac{4}{5}$ of the remaining amount. Therefore:
   $$ \text{Savings} = \frac{4}{5} \times 105000 $$
   Calculating this gives:
   $$ \text{Savings} = 84000 $$