Understanding the Ratio of Boys to Girls in a School

The problem provides us with a ratio representing the proportion of boys to girls in a school. It also gives us information about the numerical difference between the number of girls and boys. We need to use this information to find the actual number of boys.

Setting up the Problem with Ratios

The ratio of the number of boys to that of the girls is given as 11 ∶ 15.

This means for every 11 boys, there are 15 girls.

To represent the actual numbers while maintaining this ratio, we can introduce a common multiplier, let's call it \(x\). So, we can say:

• Number of boys = \(11x\)
• Number of girls = \(15x\)

Using the Difference Information

We are told that there are 200 more girls than boys in the school.

This can be written as an equation:

Number of girls - Number of boys = 200

Forming and Solving the Equation

Now, substitute the expressions for the number of boys and girls in terms of \(x\) into the equation:

\(15x - 11x = 200\)

Combine the terms with \(x\):

\(4x = 200\)

To find the value of \(x\), divide both sides of the equation by 4:

\(x = \frac{200}{4}\)

\(x = 50\)

Calculating the Number of Boys

We found that the common multiplier \(x\) is 50.

The number of boys is given by \(11x\).

Substitute the value of \(x\):

Number of boys = \(11 \times 50\)

Number of boys = 550

Let's also find the number of girls to check our work:

Number of girls = \(15x = 15 \times 50 = 750\)

Difference between girls and boys = \(750 - 550 = 200\). This matches the information given in the question.

Therefore, the number of boys in the school is 550.

Summary of the Calculation

Revision Table: School Ratio Problem

Reviewing the key elements of solving this type of ratio problem:

• Identify the given ratio (Boys : Girls = 11 : 15).
• Represent the quantities using the ratio and a variable (\(11x\) and \(15x\)).
• Identify the numerical relationship between the quantities (Girls are 200 more than Boys).
• Set up an equation based on this relationship (\(15x - 11x = 200\)).
• Solve the equation for the variable \(x\).
• Substitute the value of \(x\) back into the expressions for the quantities to find the actual numbers.

Additional Information: Ratios in Mathematics

A ratio is a comparison of two or more quantities. It shows how much of one quantity there is compared to another quantity. Ratios can be written in a few ways:

• Using a colon (:) - \(a : b\)
• As a fraction - \(\frac{a}{b}\)
• Using the word "to" - \(a\) to \(b\)

In this problem, the ratio 11:15 means that for every 11 units of boys, there are 15 units of girls. By using a common multiplier \(x\), we convert the ratio into actual comparable quantities (\(11x\) and \(15x\)). This allows us to set up algebraic equations based on other given information, such as the difference or sum of the quantities.