Calculating Monthly Salary and Expenses: A Daily Cost-Saving Analysis

Knowing how to manage your monthly salary efficiently is crucial for financial planning. This article walks you through a detailed example where we follow Yaw to understand how he distributes his monthly salary among food, rent, and drinks. We will calculate Yaw's monthly salary, the amount he spends on food, and the amount he spends on rent.

Introduction

This example demonstrates a step-by-step method to allocate a monthly salary efficiently. We will use Yaw's scenario to illustrate how to manage finances by spending a certain fraction of his income on various expenses.

Step 1: Determine the Monthly Salary

Step 1: Spending on Food

Yaw spends (frac{2}{5}) of his monthly salary on food.

( text{Amount spent on food} frac{2}{5}S )

( text{Remaining salary after spending on food} S - frac{2}{5}S frac{3}{5}S )

Step 2: Allocating Rent

Step 2: Spending on Rent

Yaw then spends (frac{1}{2}) of the remaining amount on rent.

( text{Amount spent on rent} frac{1}{2} left(frac{3}{5}Sright) frac{3}{10}S )

( text{Remaining salary after spending on rent} frac{3}{5}S - frac{3}{10}S )

To subtract these fractions, we need a common denominator which is 10:

(frac{3}{5}S frac{6}{10}S)

( text{Remaining} frac{6}{10}S - frac{3}{10}S frac{3}{10}S )

Step 3: Spending on Drinks

Step 3: Spending on Drinks

Yaw spends (frac{1}{4}) of what still remained on drinks.

( text{Amount spent on drinks} frac{1}{4} left(frac{3}{10}Sright) frac{3}{40}S )

( text{Remaining salary after spending on drinks} frac{3}{10}S - frac{3}{40}S )

To subtract these fractions, we need a common denominator which is 40:

(frac{3}{10}S frac{12}{40}S )

( text{Remaining} frac{12}{40}S - frac{3}{40}S frac{9}{40}S )

Step 4: Establishing the Equation

According to the problem, Yaw has ￠80 left.

( frac{9}{40}S 80 )

Step 5: Solving for the Monthly Salary

To find (S), multiply both sides by 40:

9S 80 times 40

9S 3200

Now, divide both sides by 9:

(S frac{3200}{9} approx 355.56)

Hence, Yaw's monthly salary is approximately ￠355.56.

Step 6: Calculating the Amounts Spent

Monthly Salary: ￠355.56

Amount Spent on Food:

( text{Food} frac{2}{5}S frac{2}{5} times frac{3200}{9} frac{640}{9} approx 71.11 )

Hence, the amount spent on food is approximately ￠71.11.

Amount Spent on Rent:

( text{Rent} frac{3}{10}S frac{3}{10} times frac{3200}{9} frac{960}{9} approx 106.67 )

Hence, the amount spent on rent is approximately ￠106.67.

Conclusion

Through this detailed example, we have successfully determined Yaw's monthly salary and allocated his expenses. Understanding how to effectively manage your finances is key to achieving long-term financial stability. The ability to track and allocate your income based on percentages can help you stay on top of your budget and save for the future.