**Unveiling the Mystery: 21 is 35% of Which Number?**

In the realm of numbers and equations, certain numerical relationships can pose a challenge to our problem-solving abilities. One such intriguing puzzle is “21 is 35% of what number?” It’s time to embark on a journey of mathematical exploration to uncover the answer.

**The Challenges and Opportunities of Mathematical Mysteries**

Navigating mathematical enigmas can often lead to feelings of frustration and perplexity. These challenges present an opportunity for growth and the satisfaction of finding solutions. Embracing these complexities leads to a deeper understanding of mathematical concepts and a sense of accomplishment.

**The Solution: Unveiling the Enigma**

After careful consideration and analysis, we arrive at the answer to the perplexing question: “21 is 35% of what number?” The solution is 60. This means that 21 constitutes 35% of 60, expressing a proportional relationship between these values.

**Key Points and Mathematical Insights**

- Determining the solution to “21 is 35% of what number?” requires patience and a systematic approach.
- The formula is: (21/35)*100 = 60.
- The answer, 60, signifies that 21 comprises 35% of 60.
- Mathematical principles allow us to find solutions to numerical puzzles.

**21 is 35% of What Number? Solving Proportional Relationships**

Mathematics is a fascinating subject that allows us to understand the relationships between quantities and solve problems using logical reasoning. Proportions are one such concept that plays a crucial role in various mathematical applications, including solving percentage problems. In this article, we will explore what it means when 21 is 35% of a number and how to determine the value of that number using proportional reasoning.

**Understanding Percentages**

Before delving into the problem, it is essential to have a clear understanding of percentages. A percentage is a mathematical way of expressing a part of something in relation to the whole. It is typically denoted by the symbol “%”. For instance, 35% represents 35 parts out of 100 equal parts.

**Proportional Relationships and Percentages**

Proportional relationships are mathematical equations that state that two ratios are equal. In the context of percentages, we can establish a proportion to determine the value of the whole when a part and its percentage are known. The formula for this proportion is:

```
Part / Whole = Percentage / 100
```

This formula allows us to solve various types of percentage problems, including finding the whole when a part and its percentage are given.

**Solving the Problem: 21 is 35% of What Number?**

Now, let’s apply the concept of proportional relationships to solve the problem at hand: 21 is 35% of what number? We can set up the proportion as follows:

```
21 / Whole = 35 / 100
```

To solve for the whole, we can cross-multiply the terms in the proportion:

```
21 x 100 = 35 x Whole
```

Simplifying the equation further, we get:

```
2100 = 35 x Whole
```

To isolate the whole, we can divide both sides of the equation by 35:

```
Whole = 2100 / 35
```

```
Whole = 60
```

Therefore, the number of which 21 is 35% is 60.

**Additional Examples of Percentage Problems**

**Example 1:**If 25% of a number is 15, what is the number?

**Answer:** Using the proportion formula, we can solve for the number:

```
15 / Number = 25 / 100
```

Cross-multiplying and simplifying, we get:

```
1500 = 25 x Number
```

```
Number = 1500 / 25
```

```
Number = 60
```

Therefore, the number is 60.

**Example 2:**A store offers a 20% discount on a product originally priced at $100. What is the discounted price?

**Answer:** To calculate the discounted price, we can apply the proportion:

```
Discounted Price / $100 = 20 / 100
```

Cross-multiplying and simplifying, we get:

```
Discounted Price x 100 = $100 x 20
```

```
Discounted Price = $100 x 20 / 100
```

```
Discounted Price = $20
```

Therefore, the discounted price is $20.

**Conclusion**

Proportional relationships are powerful mathematical tools that allow us to solve a wide range of problems, including those involving percentages. By understanding the concept of proportions and applying them correctly, we can efficiently determine the value of unknown quantities when certain parts and percentages are provided. This skill is valuable in various fields, including finance, economics, and scientific research.

**FAQs:**

**What is the formula for solving percentage problems using proportions?**

```
Part / Whole = Percentage / 100
```

**How do you find the whole when a part and its percentage are given?**

To find the whole, you can set up a proportion and cross-multiply to solve for the unknown quantity.

**What is the number of which 21 is 35%?**

The number of which 21 is 35% is 60.

**How do you calculate the discounted price of a product given its original price and discount percentage?**

To calculate the discounted price, you can set up a proportion and solve for the unknown quantity.

**What is the significance of proportional relationships in mathematics?**

Proportional relationships are significant in mathematics as they allow us to solve various types of problems involving ratios and percentages. They are also used in geometry, algebra, and calculus.

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