30 % 30\% 30% Of B B B Is Greater Than 20 % 20\% 20% Of 100.

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Problem Explanation

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The problem states that $30\%$ of a certain number $b$ is greater than $20\%$ of 100. We need to find the value of $b$ that satisfies this condition.

Step 1: Understand the Problem

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To solve this problem, we need to understand what it means to find $30\%$ of a number and $20\%$ of a number. $30\%$ of a number means multiplying the number by $0.3$, and $20\%$ of a number means multiplying the number by $0.2$.

Step 2: Translate the Problem into an Equation

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Let's translate the problem into an equation. We know that $30\%$ of $b$ is greater than $20\%$ of 100, so we can write the equation as:

$$0.3b > 0.2(100)$$

Step 3: Simplify the Equation

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Now, let's simplify the equation by evaluating the expression on the right-hand side:

$$0.3b > 20$$

Step 4: Solve for $b$

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To solve for $b$, we need to isolate $b$ on one side of the inequality. We can do this by dividing both sides of the inequality by $0.3$:

$$b > \frac{20}{0.3}$$

Step 5: Evaluate the Expression

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Now, let's evaluate the expression on the right-hand side:

$$b > \frac{20}{0.3} = 66.67$$

Step 6: Conclusion

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Therefore, the value of $b$ must be greater than $66.67$ in order to satisfy the condition that $30\%$ of $b$ is greater than $20\%$ of 100.

Example Use Case

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This problem can be used to illustrate the concept of percentages and how to solve inequalities involving percentages. For example, a business owner may want to know how much money they need to make in order to earn a certain percentage of profit.

Real-World Application

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This problem has real-world applications in finance, economics, and business. For example, a company may want to know how much revenue they need to generate in order to earn a certain percentage of profit.

Conclusion

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In conclusion, the value of $b$ must be greater than $66.67$ in order to satisfy the condition that $30\%$ of $b$ is greater than $20\%$ of 100. This problem can be used to illustrate the concept of percentages and how to solve inequalities involving percentages.

Step-by-Step Solution

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1. Understand the problem and translate it into an equation.
2. Simplify the equation by evaluating the expression on the right-hand side.
3. Solve for $b$ by isolating $b$ on one side of the inequality.
4. Evaluate the expression on the right-hand side.
5. Conclusion: the value of $b$ must be greater than $66.67$.

Key Concepts

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• Percentages: $30\%$ and $20\%$
• Inequalities: $0.3b > 0.2(100)$
• Solving for $b$: $b > \frac{20}{0.3}$

Related Problems

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• $25\%$ of $x$ is greater than $15\%$ of 200.
• $40\%$ of $y$ is less than $30\%$ of 300.

Further Reading

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• Percentages
• Inequalities
• Algebra

References

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• Mathematics
• Algebra
• Percentages
  

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Q: What is the value of $b$ that satisfies the condition that $30\%$ of $b$ is greater than $20\%$ of 100?

A: The value of $b$ must be greater than $66.67$.

Q: How do I calculate $30\%$ of a number?

A: To calculate $30\%$ of a number, multiply the number by $0.3$.

Q: How do I calculate $20\%$ of a number?

A: To calculate $20\%$ of a number, multiply the number by $0.2$.

Q: What is the equation that represents the condition that $30\%$ of $b$ is greater than $20\%$ of 100?

A: The equation is $0.3b > 0.2(100)$.

Q: How do I simplify the equation $0.3b > 0.2(100)$?

A: To simplify the equation, evaluate the expression on the right-hand side: $0.3b > 20$.

Q: How do I solve for $b$ in the equation $0.3b > 20$?

A: To solve for $b$, divide both sides of the inequality by $0.3$: $b > \frac{20}{0.3}$.

Q: What is the value of $\frac{20}{0.3}$?

A: The value of $\frac{20}{0.3}$ is $66.67$.

Q: What is the conclusion of the problem?

A: The value of $b$ must be greater than $66.67$ in order to satisfy the condition that $30\%$ of $b$ is greater than $20\%$ of 100.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in finance, economics, and business. For example, a company may want to know how much revenue they need to generate in order to earn a certain percentage of profit.

Q: How do I use this problem to illustrate the concept of percentages?

A: This problem can be used to illustrate the concept of percentages and how to solve inequalities involving percentages.

Q: What are some related problems to this one?

A: Some related problems include:

• $25\%$ of $x$ is greater than $15\%$ of 200.
• $40\%$ of $y$ is less than $30\%$ of 300.

Q: Where can I find more information on percentages and inequalities?

A: You can find more information on percentages and inequalities on websites such as Wikipedia or Khan Academy.

Q&A Summary

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• Q: What is the value of $b$ that satisfies the condition that $30\%$ of $b$ is greater than $20\%$ of 100? A: The value of $b$ must be greater than $66.67$.
• Q: How do I calculate $30\%$ of a number? A: To calculate $30\%$ of a number, multiply the number by $0.3$.
• Q: How do I calculate $20\%$ of a number? A: To calculate $20\%$ of a number, multiply the number by $0.2$.

Q&A References

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• Percentages
• Inequalities
• Algebra

Q&A Further Reading

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• Mathematics
• Algebra
• Percentages