Wei Has $$ 150.00 150.00 150.00 $ To Make A Garland Using 60-cent Balloons. He Wants To Purchase 100 Blue Balloons And Some Number Of White Balloons. He Learns That The White Balloons Are On Sale For Half Price. He Writes And Solves An Equation To
Wei's Garland Equation: A Math Problem
Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to determine the maximum number of white balloons he can buy.
Understanding the Problem
Wei's goal is to create a garland using 60-cent balloons. He has a budget of $150.00 and wants to buy 100 blue balloons and some number of white balloons. The white balloons are on sale for half price, which means they cost 30 cents each. Wei needs to determine the maximum number of white balloons he can buy within his budget.
Writing the Equation
Let's denote the number of white balloons as x. Since the white balloons are on sale for half price, the cost of each white balloon is 30 cents. The total cost of the white balloons is 30x cents. The cost of the blue balloons is 100 x 60 cents = $60.00. The total cost of the garland is the sum of the cost of the blue balloons and the white balloons, which is 30x + 60.
Wei's budget is $150.00, so the total cost of the garland must be less than or equal to $150.00. We can write an equation to represent this situation:
30x + 60 ≤ 150
Solving the Equation
To solve the equation, we need to isolate the variable x. We can start by subtracting 60 from both sides of the equation:
30x ≤ 150 - 60 30x ≤ 90
Next, we can divide both sides of the equation by 30:
x ≤ 90 / 30 x ≤ 3
Interpreting the Results
The solution to the equation is x ≤ 3. This means that Wei can buy at most 3 white balloons within his budget of $150.00. If he buys 3 white balloons, the total cost of the garland will be:
30(3) + 60 = 90 + 60 = 150
This is equal to Wei's budget, so he can buy 3 white balloons and still have enough money to buy 100 blue balloons.
Conclusion
Wei's garland equation is a simple math problem that requires us to write and solve an equation. By understanding the problem and writing the equation, we can determine the maximum number of white balloons Wei can buy within his budget. The solution to the equation is x ≤ 3, which means Wei can buy at most 3 white balloons.
Real-World Applications
This problem has real-world applications in finance and economics. When making financial decisions, it's essential to consider the cost of each item and the total cost of the purchase. By writing and solving equations, we can determine the maximum amount we can spend on each item and still stay within our budget.
Tips and Tricks
When solving equations, it's essential to follow the order of operations (PEMDAS):
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
By following the order of operations, we can ensure that our equations are solved correctly and accurately.
Common Mistakes
When solving equations, it's easy to make mistakes. Here are some common mistakes to avoid:
- Not following the order of operations (PEMDAS)
- Not isolating the variable correctly
- Not checking the solution for extraneous solutions
By avoiding these common mistakes, we can ensure that our equations are solved correctly and accurately.
Conclusion
Wei's garland equation is a simple math problem that requires us to write and solve an equation. By understanding the problem and writing the equation, we can determine the maximum number of white balloons Wei can buy within his budget. The solution to the equation is x ≤ 3, which means Wei can buy at most 3 white balloons. This problem has real-world applications in finance and economics, and by following the order of operations and avoiding common mistakes, we can ensure that our equations are solved correctly and accurately.
Wei's Garland Equation: A Math Problem Q&A
In our previous article, we explored Wei's garland equation and determined the maximum number of white balloons he can buy within his budget of $150.00. In this article, we'll answer some frequently asked questions about the problem and provide additional insights.
Q: What is the cost of each white balloon?
A: The cost of each white balloon is 30 cents, since they are on sale for half price.
Q: How many blue balloons can Wei buy?
A: Wei can buy 100 blue balloons, which cost 60 cents each.
Q: What is the total cost of the blue balloons?
A: The total cost of the blue balloons is 100 x 60 cents = $60.00.
Q: What is the total cost of the white balloons?
A: The total cost of the white balloons is 30x cents, where x is the number of white balloons.
Q: How do we determine the maximum number of white balloons Wei can buy?
A: We can determine the maximum number of white balloons Wei can buy by solving the equation 30x + 60 ≤ 150.
Q: What is the solution to the equation?
A: The solution to the equation is x ≤ 3, which means Wei can buy at most 3 white balloons.
Q: What happens if Wei buys more than 3 white balloons?
A: If Wei buys more than 3 white balloons, the total cost of the garland will exceed his budget of $150.00.
Q: Can Wei buy any number of white balloons?
A: No, Wei can only buy at most 3 white balloons within his budget of $150.00.
Q: What is the total cost of the garland if Wei buys 3 white balloons?
A: The total cost of the garland if Wei buys 3 white balloons is 30(3) + 60 = 90 + 60 = 150.
Q: Is this equal to Wei's budget?
A: Yes, this is equal to Wei's budget of $150.00.
Q: What is the significance of the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is essential when solving equations. It ensures that we evaluate expressions in the correct order and avoid errors.
Q: What are some common mistakes to avoid when solving equations?
A: Some common mistakes to avoid when solving equations include not following the order of operations (PEMDAS), not isolating the variable correctly, and not checking the solution for extraneous solutions.
Q: Can you provide an example of an extraneous solution?
A: Yes, an example of an extraneous solution is x = 4, which is not a valid solution to the equation 30x + 60 ≤ 150.
Q: Why is it essential to check for extraneous solutions?
A: It's essential to check for extraneous solutions because they can lead to incorrect conclusions and mistakes.
Conclusion
In this article, we've answered some frequently asked questions about Wei's garland equation and provided additional insights. We've discussed the cost of each white balloon, the total cost of the blue balloons, and the total cost of the white balloons. We've also determined the maximum number of white balloons Wei can buy within his budget of $150.00. By following the order of operations (PEMDAS) and avoiding common mistakes, we can ensure that our equations are solved correctly and accurately.
Additional Resources
For more information on solving equations and the order of operations (PEMDAS), please refer to the following resources:
- Khan Academy: Solving Equations
- Mathway: Order of Operations (PEMDAS)
- IXL: Solving Equations
Practice Problems
Try solving the following practice problems to test your skills:
- Solve the equation 2x + 5 ≤ 11.
- Solve the equation x - 3 ≥ 7.
- Solve the equation 4x + 2 ≤ 18.
Conclusion
In conclusion, Wei's garland equation is a simple math problem that requires us to write and solve an equation. By understanding the problem and writing the equation, we can determine the maximum number of white balloons Wei can buy within his budget. The solution to the equation is x ≤ 3, which means Wei can buy at most 3 white balloons. By following the order of operations (PEMDAS) and avoiding common mistakes, we can ensure that our equations are solved correctly and accurately.