Solving Ratio Problems: Calculating the Number of English Books

When dealing with book ratios in a shop setting, it's crucial to understand how to use these ratios to find the exact number of books of any given type. This article will guide you through the process of solving a specific problem where the ratio of maths, English, and science books is given. We'll walk you through step-by-step calculations to find the number of English books when the shop has 140 science books.

Understanding the Problem

The ratio of maths, English, and science books in a shop is given as 5:12:7. This means that for every 5 maths books, there are 12 English books and 7 science books. The problem involves finding out how many English books are present in the shop if there are 140 science books.

Breaking Down the Ratio

The first step in solving this problem is to understand the total number of parts in the given ratio. The breakdown is as follows:

Ratio Parts

MATHS: 5 parts ENGLISH: 12 parts SCIENCE: 7 parts

The total number of parts is 5 12 7 24.

Calculating the Value of One Part

Since there are 140 science books, and these books correspond to the 7 parts in the ratio, we can find the value of one part by dividing the number of science books by the number of parts they represent:

Value of One Part

(text{Value of one part} frac{140}{7} 20)

Calculating the Number of English Books

Now, using the value of one part, we can easily find the number of English books by multiplying the value of one part by the number of parts that correspond to English books:

Number of English Books

(text{Number of English books} 12 times 20 240)

Alternative Method

Here's another method to reach the same result:

Find the total number of books in the shop: (text{Total number of books} frac{140 times 24}{7} 20 times 24 480) Calculate the number of English books using the ratio: (text{Number of English books} frac{12}{24} times 480 240)

Conclusion

Therefore, the number of English books in the shop is 240. Understanding and applying these steps can make similar ratio problems much simpler. Whether you're a student, a shopkeeper, or simply someone who enjoys solving puzzles, mastering the art of ratio calculations can be a valuable skill.

Additional Tips for Solving Ratio Problems

Understand the given ratio and break it down into its component parts. Calculate the value of one part by dividing the given quantity by the number of parts it represents. Multiply the value of one part by the number of parts for the desired quantity to find the answer. Double-check your calculations to ensure accuracy.

Feel free to explore various problems involving ratios and practice different methods to solve them. With consistent practice, you'll become more proficient and quicker in handling such problems.