There Are Boys And Girls In A Class In The Ratio 13:14 There Are 135 Pupils In Total. Calculate The Number Of Girls.
Introduction
In this problem, we are given a ratio of boys to girls in a class as 13:14 and the total number of pupils in the class is 135. We need to find the number of girls in the class.
Understanding the Ratio
The given ratio of boys to girls is 13:14. This means that for every 13 boys, there are 14 girls in the class. We can represent this ratio as a fraction, where the number of boys is 13x and the number of girls is 14x, where x is a common multiplier.
Calculating the Total Number of Pupils
We are given that the total number of pupils in the class is 135. We can set up an equation using the ratio and the total number of pupils to find the value of x.
Let's assume the number of boys is 13x and the number of girls is 14x. The total number of pupils is the sum of the number of boys and the number of girls, which is 13x + 14x = 27x.
Since the total number of pupils is 135, we can set up the equation:
27x = 135
Solving for x
To find the value of x, we can divide both sides of the equation by 27:
x = 135 / 27
x = 5
Finding the Number of Girls
Now that we have found the value of x, we can find the number of girls by multiplying the value of x by 14:
Number of girls = 14x = 14(5) = 70
Conclusion
Therefore, the number of girls in the class is 70.
Step-by-Step Solution
Here's a step-by-step solution to the problem:
- Understand the given ratio of boys to girls.
- Represent the ratio as a fraction, where the number of boys is 13x and the number of girls is 14x.
- Set up an equation using the ratio and the total number of pupils to find the value of x.
- Solve for x by dividing both sides of the equation by 27.
- Find the number of girls by multiplying the value of x by 14.
Tips and Tricks
- When dealing with ratios, it's essential to understand the concept of equivalent ratios.
- When setting up an equation, make sure to use the correct variables and constants.
- When solving for x, make sure to perform the correct operations, such as division.
Real-World Applications
This problem can be applied to real-world scenarios, such as:
- Calculating the number of boys and girls in a class based on a given ratio.
- Determining the number of students in a school based on a given ratio of boys to girls.
- Understanding the concept of equivalent ratios in real-world applications.
Conclusion
In conclusion, the number of girls in the class is 70. This problem requires a deep understanding of ratios and equivalent ratios. By following the step-by-step solution, you can easily calculate the number of girls in the class based on the given ratio and total number of pupils.
Q&A: Calculating the Number of Girls in a Class
Q: What is the given ratio of boys to girls in the class?
A: The given ratio of boys to girls in the class is 13:14.
Q: What is the total number of pupils in the class?
A: The total number of pupils in the class is 135.
Q: How can we represent the ratio of boys to girls in the class?
A: We can represent the ratio of boys to girls in the class as 13x:14x, where x is a common multiplier.
Q: What is the equation to find the value of x?
A: The equation to find the value of x is 27x = 135.
Q: How can we solve for x?
A: We can solve for x by dividing both sides of the equation by 27.
Q: What is the value of x?
A: The value of x is 5.
Q: How can we find the number of girls in the class?
A: We can find the number of girls in the class by multiplying the value of x by 14.
Q: What is the number of girls in the class?
A: The number of girls in the class is 70.
Q: What is the significance of the ratio 13:14 in this problem?
A: The ratio 13:14 represents the number of boys to girls in the class. This ratio is essential in calculating the number of girls in the class.
Q: How can we apply this problem to real-world scenarios?
A: We can apply this problem to real-world scenarios, such as calculating the number of boys and girls in a class based on a given ratio, determining the number of students in a school based on a given ratio of boys to girls, and understanding the concept of equivalent ratios in real-world applications.
Q: What are some tips and tricks for solving this problem?
A: Some tips and tricks for solving this problem include understanding the concept of equivalent ratios, setting up the correct equation, and performing the correct operations to solve for x.
Q: What are some common mistakes to avoid when solving this problem?
A: Some common mistakes to avoid when solving this problem include not understanding the concept of equivalent ratios, not setting up the correct equation, and not performing the correct operations to solve for x.
Q: How can we verify the solution to this problem?
A: We can verify the solution to this problem by plugging in the values of x and the ratio of boys to girls into the equation and checking if the result is correct.
Q: What are some real-world applications of this problem?
A: Some real-world applications of this problem include calculating the number of boys and girls in a class based on a given ratio, determining the number of students in a school based on a given ratio of boys to girls, and understanding the concept of equivalent ratios in real-world applications.
Conclusion
In conclusion, the number of girls in the class is 70. This problem requires a deep understanding of ratios and equivalent ratios. By following the step-by-step solution and understanding the Q&A, you can easily calculate the number of girls in the class based on the given ratio and total number of pupils.