**Understanding the Mathematical Equation: 49 is 70% of What Number?**

In the realm of mathematics, percentages and proportions often pose challenges. One such puzzle is unraveling the mystery behind the equation “49 is 70% of what number?” This conundrum can evoke a sense of curiosity and frustration, as we grapple to find its solution.

**The Struggle to Uncover the Unknown**

When confronted with such an equation, it’s natural to feel bewildered. The unknown variable looms large, casting a shadow over our understanding. We may feel lost in a labyrinth of numbers, unsure of which path to take. This uncertainty can lead to frustration and a desire to unravel the mystery.

**The Mathematical Landscape**

To solve the equation “49 is 70% of what number,” we must employ the concept of percentages. A percentage represents a fraction of a hundred, and it can be expressed in decimal form by dividing it by 100. In this case, 70% is equivalent to 0.7. So, we can rewrite the equation as:

```
49 = 0.7 * x
```

where x represents the unknown number.

**Solving for the Unknown**

To solve for x, we simply divide both sides of the equation by 0.7:

```
x = 49 / 0.7
```

```
x = 70
```

Therefore, the number that 49 is 70% of is 70.

## 49 is 70 of What Number?

### Determining the Unknown Value

In mathematical equations, percentages are used to represent parts of a whole. When we know the percentage and the part, we can determine the whole using the formula:

```
Whole = Part / (Percentage / 100)
```

In this case, we are given that 49 is 70% of an unknown number. We can solve for the unknown number by substituting the values into the formula:

```
Whole = 49 / (70 / 100)
```

```
Whole = 49 / 0.7
```

```
Whole = 70
```

### Explanation

Therefore, 49 is 70% of 70. This means that the unknown number is **70**.

### Related Concepts

- Percentage: A representation of a part of a whole as a fraction of 100.
- Ratio: A comparison of two quantities expressed as a fraction or decimal.
- Proportion: A statement that two ratios are equal.

### Applications

Understanding percentages and proportions is essential in various fields, including:

- Finance: Calculating interest rates, discounts, and taxes.
- Science: Expressing measurements, concentrations, and probabilities.
- Engineering: Determining ratios of materials, forces, and dimensions.
- Daily Life: Comparing prices, estimating quantities, and making decisions.

### Examples

**Example 1:**

If a store offers a 20% discount on a product priced at $50, what is the discounted price?

**Solution:**

```
Discounted Price = 50 - (20 / 100) * 50
```

```
Discounted Price = 50 - 10
```

```
Discounted Price = $40
```

**Example 2:**

A recipe calls for 1 cup of flour and 2 cups of water. If you want to make a smaller batch, what ratio of flour to water should you use?

**Solution:**

```
Ratio = 1 cup of flour / 2 cups of water
```

```
Ratio = 1:2
```

This ratio can be simplified to 1:2, meaning you should use 1 part flour for every 2 parts water, regardless of the batch size.

### Conclusion

Percentages and proportions are fundamental mathematical concepts used to compare quantities and solve problems involving parts of a whole. Understanding these concepts is essential for success in various fields and everyday life.

### FAQs

**What is the formula for finding the percentage of a number?**

- Percentage = (Part / Whole) * 100%

**How do you convert a percentage to a decimal?**

- Divide the percentage by 100.

**What is a proportion?**

- A statement that two ratios are equal.

**How can I solve a ratio problem?**

- Set up two equal ratios and solve for the unknown variable.

**Where are percentages and proportions used in everyday life?**

- Comparing prices, estimating quantities, and making decisions.

.

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