Problem 54 - Algebra for College Students

Question

In a flock of 30 geese, 15 are male. What percent are not male?

Step-by-Step Solution

Answer

50% of the geese are not male.

Step 1: Determine the total number of geese

The problem states that there is a total of 30 geese.

Step 2: Identify the number of male geese

Out of the total 30 geese, 15 are identified as male.

Step 3: Calculate the number of geese that are not male

To find the number of geese that are not male, subtract the number of male geese from the total number of geese: 30 - 15 = 15 geese that are not male.

Step 4: Calculate the percentage of geese that are not male

To determine the percentage, use the formula: \(\text{Percentage} = \frac{\text{Number of non-male geese}}{\text{Total number of geese}} \times 100\)\(\text{Percentage} = \frac{15}{30} \times 100\)Simplifying this, \(\text{Percentage} = 50\%\).

Key Concepts

Basic Arithmetic

Understanding basic arithmetic is crucial for solving percentage problems. This includes simple operations like addition, subtraction, multiplication, and division. In the given exercise, you first determine the total number of geese and then identify the number of male geese. By subtracting the number of male geese from the total, you find the number of geese that are not male. These steps involve basic arithmetic operations that form the foundation of more complex calculations.
Example steps:

• Addition: 15 male geese + 15 non-male geese = total 30 geese
• Subtraction: 30 total geese - 15 male geese = 15 non-male geese

These operations are straightforward but essential for accurate problem-solving.

Percentage

Percentage is another essential concept in this problem. A percentage represents a fraction of 100. The formula for calculating percentages is: \(\text{Percentage} = \frac{\text{Part}}{\text{Total}} \times 100\).
Applying this to our exercise:

• First, identify your 'Part' (non-male geese), which is 15.
• Then identify your 'Total' (total geese), which is 30.

The formula becomes: \(\text{Percentage} = \frac{15}{30} \times 100\).
Simplify the fraction: \(\frac{15}{30} = 0.5\)
Finally, multiply by 100 to get the percentage: \(0.5 \times 100 = 50\%\).
This tells you that 50% of the geese are not male.

Problem Solving

Problem-solving involves breaking down complex problems into manageable steps. Here’s how you can systematically solve a problem like the one in the exercise:

• Step 1: Understand the problem statement. Identify the total number of elements (in this case, 30 geese) and the subset you're interested in (15 are male).
• Step 2: Apply relevant basic arithmetic to find the required values. Here, subtract the number of male geese from the total to get the number of non-male geese.
• Step 3: Use the percentage formula to translate your findings into a percentage.
• Step 4: Simplify and verify your calculation to ensure accuracy.

By following these systematic steps, complex problems become easier to solve. For example, in our exercise, once you subtract the male geese from the total, and divide the non-male geese by the total, you multiply by 100 to get the percentage. Confirming your understanding at each step helps to avoid mistakes and builds strong problem-solving skills.