Solving the Ratio Puzzle: How Many Novels Were Bought When Adjusting the Ratio?

When dealing with ratio problems, it's crucial to understand how to manipulate and adjust given ratios to find unknown quantities. This article will walk you through a specific example involving an online library where the initial ratio of novels to dictionaries changes over time. Let's dive into the details and solve the puzzle of how many more novels were bought to change the ratio.

Understanding the Initial Conditions

Given the initial conditions in our example, the online library has a specific ratio of novels to dictionaries. This ratio is 2:3. This means for every 2 novels, there are 3 dictionaries in the library. We are also told that the total number of novels is 624.

Calculating the Initial Number of Dictionaries

Given the ratio of novels to dictionaries, ( n : d 2 : 3 ), and the total number of novels is 624:

Let ( n 2x ) and ( d 3x ), where ( x ) is a common multiple of the two quantities.

Since the total number of novels is 624, we have:

2x 624

Solving for ( x ):

x 624 / 2

x 312

Now we can find the number of dictionaries:

d 3 * 312 936

So, initially, the library has 624 novels and 936 dictionaries.

Adjusting the Ratio of Novels to Dictionaries

Joe buys more novels, altering the initial ratio to 7:3. We need to determine how many more novels were bought to achieve this new ratio.

Calculating the New Number of Novels

Let's denote the new number of novels as ( N ). According to the new ratio, 7 out of every 10 parts are novels, and 3 out of every 10 parts are dictionaries. The number of dictionaries will still be 936, as stated in the problem.

Using the new ratio ( N : D 7 : 3 ), and knowing D (dictionaries) 936:

N / 936 7 / 3

3N 7 * 936

3N 6552

N 6552 / 3

N 2184

So, after Joe's purchase, the library has a total of 2184 novels.

Conclusion: How Many Novels Were Bought?

To find out how many novels Joe bought, we subtract the initial number of novels from the new total number of novels:

2184 - 624 1560

Therefore, Joe bought 1560 novels to adjust the ratio from 2:3 to 7:3 in the online library.

Practical Application of Ratio Problems

Understanding and solving such ratio problems is crucial for various applications, from managing resources in a library to scaling up or down in business operations. By mastering these techniques, one can efficiently manage data and resources in a wide range of scenarios.

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