Problem 108 - Elementary Algebra

Question

Dimple gets paid \(\$ 3,200\) per month. She pays \(\$ 960\) a month for rent. What percent of her monthly pay goes to rent?

Step-by-Step Solution

Answer

30%

Step 1: Determine Monthly Pay

Dimple earns \( \$ 3,200 \) per month.

Step 2: Determine Monthly Rent Payment

Dimple pays \( \$ 960 \) per month for rent.

Step 3: Set Up the Percentage Formula

The formula to find the percentage is \[ \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \]. Here, the \text{Part} is \( \$ 960 \), and the \text{Whole} is \( \$ 3,200 \).

Step 4: Substitute Values into the Formula

Substitute \( \$ 960 \) for the part and \( \$ 3,200 \) for the whole: \[ \text{Percent} = \frac{960}{3200} \times 100 \]

Step 5: Simplify the Fraction

Simplify \( \frac{960}{3200} \) to \( \frac{3}{10} \) or \( 0.3 \).

Step 6: Calculate the Percentage

Multiply \( 0.3 \) by \( 100 \) to get \( 30 \% \).

Key Concepts

Monthly Income

Monthly income refers to the total amount of money earned by an individual in one month. It can come from different sources such as salaries, wages, or freelance work. In this problem, Dimple's monthly income is clearly stated as \( \$3,200 \). This figure is important because we use it to calculate how much of it is spent on rent.

Understanding your monthly income is essential for budgeting and financial planning. Knowing this amount helps you to:

• Plan your expenses.
• Set aside savings.
• Determine how much you can spend on non-essentials.

Rent Payment

Rent payment refers to the money paid by a tenant to a landlord in exchange for living in a property. In Dimple's case, she pays \( \$960 \) each month for rent. This amount is usually fixed and must be paid regularly, typically monthly. Rent is a significant expense for most people and often takes up a large portion of their income.

When budgeting, it's important to keep track of rent to ensure you can consistently meet this obligation without financial strain. By calculating what percentage of your income goes towards rent, you gain a clearer understanding of your budget.

The percentage formula \[ \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \] allows us to determine how much of Dimple's income is used for rent.

Fraction Simplification

Fraction simplification is the process of reducing a fraction to its simplest form. This is achieved by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).

In our example, we need to simplify the fraction \( \frac{960}{3200} \). Both numbers share common factors, so to simplify, we find their GCD and divide them by it.

Let's break it down:

• The GCD of 960 and 3200 is 320.
• Divide both the numerator and the denominator by 320.
• This gives us \( \frac{960 \div 320}{3200 \div 320} = \frac{3}{10} \).

This simplified fraction, \( \frac{3}{10} \), can also be represented as a decimal: 0.3. Finally, to convert this to a percentage, we multiply by 100, giving us 30%. Simplifying fractions helps in making calculations easier and more manageable.