Understanding Proportional Relationships: Calculating the Number of Girls in Peter's School

Proportional relationships are frequently encountered in real-life scenarios, such as in school populations. In the case of Peter's school, the gender ratio is 11 girls to 8 boys. This article will guide you through the process of calculating the number of girls when given the number of boys. We will use the example where Peter's school has 1200 boys.

Step-by-Step Solution

Given the ratio of girls to boys as 11:8, and knowing there are 1200 boys, we want to find out the number of girls. Here's a step-by-step explanation:

Step 1: Understand the Ratio

The ratio of girls to boys is 11:8, which means for every 11 girls, there are 8 boys.

Step 2: Cross-Multiplication Method

Let's set up the proportion:

[ frac{11}{8} frac{X}{1200} ]

where ( X ) is the number of girls.

Step 3: Solve for ( X )

We need to cross-multiply to find ( X ):

[ 8X 11 times 1200 ]

Calculate the product on the right side:

[ 8X 13200 ]

Now, solve for ( X ) by dividing both sides by 8:

[ X frac{13200}{8} 1650 ]

Therefore, the number of girls in Peter's school is 1650.

Alternative Method: Unitary Method

Another approach is to use the unitary method:

Calculate the value for 1 part of the ratio (8 boys in the 11:8 ratio): Then multiply by the total ratio value (11 girls) to find the number of girls.

Here's the calculation:

Divide the number of boys by the boys' part of the ratio: 1200 boys ÷ 8 boys 150 (This is 1 part of the ratio). Multiply the result by the girls' part of the ratio: 150 × 11 girls 1650 girls

Thus, the number of girls in Peter's school is 1650.

Conclusion

Understanding and solving problems involving ratios and proportions is essential in various contexts, from school enrollment to more complex scenarios in mathematics and data analysis. The method demonstrated here can be applied to similar problems, making it easier to find the unknown quantity based on given ratios and known quantities.

Related Content

Explore more content related to ratios, proportions, and problem-solving techniques in mathematics:

Ratios and Proportions in Everyday Life - Examples and real-world applications of ratios and proportions. Solving Practical Problems with Ratios and Proportions - Step-by-step guides and examples for solving various problems involving ratios. Understanding Proportional Reasoning - Comprehensive guide to proportional reasoning and its applications.