21 Is 70 Of What Number

Unlock the Mystery: Unraveling the Equation of 21 is 70 of What Number

Imagine a perplexing equation that challenges your numerical prowess: 21 is 70 of what number? It’s a mind-bender that can leave you scratching your head. But worry not, let’s embark on a journey to uncover the secret behind this enigmatic riddle.

The Quest for the Elusive Number

When faced with such numerical conundrums, it’s crucial to break down the components and understand the underlying relationship. In this case, the equation suggests that 21, the number on the left-hand side, is a fraction of an unknown number, represented by the x on the right-hand side.

Revealing the Solution

To find the elusive number, we need to isolate x on one side of the equation. Let’s begin by dividing both sides by 70. This gives us 21/70 = x. By simplifying the fraction, we arrive at the answer: x = 3.

Connecting the Dots

Therefore, the solution to the equation 21 is 70 of what number is 3. This means that 21 is 70% of 3. It’s like a puzzle piece that fits perfectly into place, revealing the interconnectedness of numbers.

Summary

To recap, 21 is 70 of the number 3. This relationship can be represented as 21/70 = x, where x simplifies to 3. Understanding the principles of fractions and ratios is key to solving such equations. Remember, with a bit of patience and number crunching, you can unlock the secrets of mathematical puzzles like these.

21 Is 70 Of What Number

21 is 70% of What Number?

Introduction:

Arithmetic proportions are essential in problem-solving, establishing relationships between quantities. This article delves into understanding the relationship between 21 and 70%, thereby determining the unknown number they represent.

1. Establishing the Equation

To find the number that 21 represents 70% of, we can set up an equation:

21 = 70% * x

where x represents the unknown number.

2. Multiplying by 100 to Convert Percentage

To solve for x, we need to convert 70% to a decimal:

70% = 70/100 = 0.7

Substituting this into our equation:

21 = 0.7 * x

3. Solving for x

Dividing both sides by 0.7, we isolate x:

x = 21 / 0.7

Calculating:

x = 30

4. Interpretation

Therefore, 21 is 70% of the number 30.

5. Cross-Checking

To verify our result, we can multiply 30 by 0.7:

0.7 * 30 = 21

Confirming that 21 is indeed 70% of 30.

6. Using a Proportion Table

An alternative method is to use a proportion table:

| Number | Percentage | Value |
|—|—|—|
| x | 100% | 30 |
| 21 | 70% | y |

The proportion of y to 30 is equal to 70 to 100. Solving for y:

y = (70/100) * 30

Calculating:

y = 21

7. Real-World Applications

Understanding proportions has practical implications:

  • Finance: Calculating interest rates and loan amounts.
  • Engineering: Scaling plans and designs.
  • Chemistry: Determining reactant and product stoichiometry.

8. Percentages and Fractions

Percentages are closely related to fractions:

Percentage = Fraction * 100

For example, 70% is the same as 70/100 = 0.7.

9. Applications in Measurement

Proportions are used in measurement conversions:

1 meter = 100 centimeters

To convert meters to centimeters, we multiply by 100.

10. Ratio and Proportion

A ratio is a relationship between two quantities, while a proportion is an equality between two ratios.

11. Solving Ratio and Proportion Problems

To solve ratio and proportion problems, we use cross-multiplication:

a/b = c/d
ad = bc

12. Applications in Geometry

Proportions are essential in geometric constructions and theorems, such as the Pythagorean theorem.

13. Similar Figures

Similar figures have the same shape but not necessarily the same size. Their corresponding sides are in proportion.

14. Scale Factors

The scale factor between two similar figures is the ratio of their corresponding sides.

15. Direct and Inverse Proportions

Direct proportions mean as one quantity increases, the other also increases. Inverse proportions mean as one quantity increases, the other decreases.

Conclusion

Understanding the relationship between 21 and 70% allowed us to determine that 21 is 70% of the number 30. Proportions and percentages are fundamental mathematical concepts with wide-ranging applications, including problem-solving, measurement conversions, and real-world scenarios.

FAQs

  1. What is a percentage?
  • A percentage represents a part of a whole expressed out of 100.
  1. How do you convert a percentage to a decimal?
  • Divide the percentage by 100.
  1. What is the relationship between ratios and proportions?
  • A proportion is an equality between two ratios.
  1. What is a scale factor?
  • A scale factor is the ratio of corresponding sides between similar figures.
  1. Name two real-world applications of proportions.
  • Calculating interest rates and scaling plans.

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