A 20 Cm Long Rod Has Painted Blue And Red. If The Painting Of This Last Color Is The Quadruple Of The Painted Blue. How Many Centimeters Will We Have To Paint Blue Again So That The Rod Is Half Blue And Half Red?
Introduction
In this problem, we are given a 20 cm long rod that has been painted blue and red. The amount of red paint is four times the amount of blue paint. We need to find out how many centimeters of blue paint need to be added to make the rod half blue and half red.
Understanding the Problem
Let's assume that the amount of blue paint initially is x cm. Since the amount of red paint is four times the amount of blue paint, the amount of red paint is 4x cm.
Setting Up the Equation
We know that the total length of the rod is 20 cm. After adding the blue paint, the total length of the rod will be 20 + x cm. Since we want the rod to be half blue and half red, the amount of blue paint should be equal to the amount of red paint. Therefore, we can set up the equation:
20 + x = 2(4x)
Solving the Equation
To solve the equation, we can start by simplifying the right-hand side:
20 + x = 8x
Next, we can subtract x from both sides:
20 = 7x
Now, we can divide both sides by 7:
x = 20/7
x = 2.86 (approximately)
Finding the Amount of Blue Paint to be Added
Since the amount of blue paint initially is x cm, we need to add 20 - x cm of blue paint to make the rod half blue and half red. Therefore, the amount of blue paint to be added is:
20 - x = 20 - 2.86 = 17.14 (approximately)
Conclusion
In this problem, we found that the amount of blue paint initially is approximately 2.86 cm. To make the rod half blue and half red, we need to add approximately 17.14 cm of blue paint.
Final Answer
The final answer is 17.14 cm.
Introduction
In this problem, we are given a 20 cm long rod that has been painted blue and red. The amount of red paint is four times the amount of blue paint. We need to find out how many centimeters of blue paint need to be added to make the rod half blue and half red.
Understanding the Problem
Let's assume that the amount of blue paint initially is x cm. Since the amount of red paint is four times the amount of blue paint, the amount of red paint is 4x cm.
Setting Up the Equation
We know that the total length of the rod is 20 cm. After adding the blue paint, the total length of the rod will be 20 + x cm. Since we want the rod to be half blue and half red, the amount of blue paint should be equal to the amount of red paint. Therefore, we can set up the equation:
20 + x = 2(4x)
Solving the Equation
To solve the equation, we can start by simplifying the right-hand side:
20 + x = 8x
Next, we can subtract x from both sides:
20 = 7x
Now, we can divide both sides by 7:
x = 20/7
x = 2.86 (approximately)
Finding the Amount of Blue Paint to be Added
Since the amount of blue paint initially is x cm, we need to add 20 - x cm of blue paint to make the rod half blue and half red. Therefore, the amount of blue paint to be added is:
20 - x = 20 - 2.86 = 17.14 (approximately)
Conclusion
In this problem, we found that the amount of blue paint initially is approximately 2.86 cm. To make the rod half blue and half red, we need to add approximately 17.14 cm of blue paint.
Final Answer
The final answer is 17.14 cm.
Q&A
Q: What is the initial amount of blue paint on the rod?
A: The initial amount of blue paint on the rod is approximately 2.86 cm.
Q: How much blue paint needs to be added to make the rod half blue and half red?
A: Approximately 17.14 cm of blue paint needs to be added to make the rod half blue and half red.
Q: What is the total length of the rod?
A: The total length of the rod is 20 cm.
Q: What is the ratio of red paint to blue paint initially?
A: The ratio of red paint to blue paint initially is 4:1.
Q: How can we determine the amount of blue paint to be added?
A: We can determine the amount of blue paint to be added by setting up an equation and solving for x.
Q: What is the equation to solve for x?
A: The equation to solve for x is 20 + x = 2(4x).
Q: How do we simplify the equation?
A: We can simplify the equation by subtracting x from both sides and then dividing both sides by 7.
Q: What is the final answer?
A: The final answer is 17.14 cm.
Additional Tips and Tricks
- When solving equations, make sure to follow the order of operations (PEMDAS).
- When simplifying equations, try to isolate the variable (x) on one side of the equation.
- When solving for x, make sure to check your units and make sure they are consistent.
Conclusion
In this article, we solved a problem involving a 20 cm long rod that has been painted blue and red. We found that the amount of blue paint initially is approximately 2.86 cm and that approximately 17.14 cm of blue paint needs to be added to make the rod half blue and half red. We also provided a Q&A section to help clarify any questions or doubts.