Twice Connie's Age Plus Half Her Mother's Age Is 48. Three Times Connie's Age Less Half Her Mother's Age Is 27. How Old Are Connie And Her Mother.
Introduction
Mathematics is a fascinating subject that involves solving problems and puzzles using logical reasoning and mathematical operations. In this article, we will explore a mathematical puzzle that involves a young girl named Connie and her mother. The puzzle states that twice Connie's age plus half her mother's age is 48, and three times Connie's age less half her mother's age is 27. Our goal is to find the ages of Connie and her mother.
Let's Break Down the Problem
To solve this puzzle, we need to break it down into two separate equations. Let's denote Connie's age as C and her mother's age as M.
The first equation states that twice Connie's age plus half her mother's age is 48. We can write this equation as:
2C + (1/2)M = 48
The second equation states that three times Connie's age less half her mother's age is 27. We can write this equation as:
3C - (1/2)M = 27
Solving the Equations
To solve these equations, we can use the method of substitution or elimination. Let's use the elimination method to eliminate the variable M.
First, we can multiply the first equation by 2 to get rid of the fraction:
4C + M = 96
Next, we can multiply the second equation by 2 to get rid of the fraction:
6C - M = 54
Now, we can add the two equations together to eliminate the variable M:
(4C + M) + (6C - M) = 96 + 54 10C = 150
Finding Connie's Age
Now that we have eliminated the variable M, we can solve for Connie's age C. We can divide both sides of the equation by 10:
C = 150/10 C = 15
So, Connie is 15 years old.
Finding Her Mother's Age
Now that we know Connie's age, we can substitute it into one of the original equations to find her mother's age. Let's use the first equation:
2C + (1/2)M = 48 2(15) + (1/2)M = 48 30 + (1/2)M = 48
Next, we can subtract 30 from both sides of the equation:
(1/2)M = 18
Finally, we can multiply both sides of the equation by 2 to solve for M:
M = 36
So, Connie's mother is 36 years old.
Conclusion
In this article, we have solved a mathematical puzzle that involved a young girl named Connie and her mother. We have used the method of substitution and elimination to find the ages of Connie and her mother. The final answer is that Connie is 15 years old and her mother is 36 years old.
Frequently Asked Questions
- Q: How did you solve the puzzle? A: We used the method of substitution and elimination to solve the puzzle.
- Q: What are the ages of Connie and her mother? A: Connie is 15 years old and her mother is 36 years old.
- Q: Can you explain the steps in more detail? A: Yes, we can explain the steps in more detail. Please let us know if you have any further questions.
Related Topics
- Algebraic equations
- Mathematical puzzles
- Problem-solving techniques
- Mathematical reasoning
References
- [1] "Algebraic Equations" by Math Open Reference
- [2] "Mathematical Puzzles" by Brilliant.org
- [3] "Problem-Solving Techniques" by Khan Academy
Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of resources.
Introduction
In our previous article, we solved a mathematical puzzle that involved a young girl named Connie and her mother. The puzzle stated that twice Connie's age plus half her mother's age is 48, and three times Connie's age less half her mother's age is 27. We used the method of substitution and elimination to find the ages of Connie and her mother. In this article, we will answer some frequently asked questions related to the puzzle.
Q&A
Q: How did you solve the puzzle?
A: We used the method of substitution and elimination to solve the puzzle. We first wrote down the two equations:
2C + (1/2)M = 48 3C - (1/2)M = 27
We then multiplied the first equation by 2 to get rid of the fraction:
4C + M = 96
Next, we multiplied the second equation by 2 to get rid of the fraction:
6C - M = 54
We then added the two equations together to eliminate the variable M:
(4C + M) + (6C - M) = 96 + 54 10C = 150
We then divided both sides of the equation by 10 to solve for C:
C = 150/10 C = 15
We then substituted C into one of the original equations to solve for M:
2C + (1/2)M = 48 2(15) + (1/2)M = 48 30 + (1/2)M = 48
We then subtracted 30 from both sides of the equation:
(1/2)M = 18
Finally, we multiplied both sides of the equation by 2 to solve for M:
M = 36
Q: What are the ages of Connie and her mother?
A: Connie is 15 years old and her mother is 36 years old.
Q: Can you explain the steps in more detail?
A: Yes, we can explain the steps in more detail. Please let us know if you have any further questions.
Q: What is the method of substitution and elimination?
A: The method of substitution and elimination is a technique used to solve systems of linear equations. It involves substituting one equation into another equation to eliminate one of the variables.
Q: What is the difference between substitution and elimination?
A: Substitution involves substituting one equation into another equation to eliminate one of the variables. Elimination involves adding or subtracting two equations to eliminate one of the variables.
Q: Can you provide more examples of mathematical puzzles?
A: Yes, we can provide more examples of mathematical puzzles. Please let us know if you have any specific requests.
Q: How can I practice solving mathematical puzzles?
A: You can practice solving mathematical puzzles by trying out different problems and techniques. You can also use online resources such as Khan Academy, Brilliant.org, and Math Open Reference to practice solving mathematical puzzles.
Conclusion
In this article, we have answered some frequently asked questions related to the mathematical puzzle that involved a young girl named Connie and her mother. We have used the method of substitution and elimination to solve the puzzle and have provided more information on how to practice solving mathematical puzzles.
Related Topics
- Algebraic equations
- Mathematical puzzles
- Problem-solving techniques
- Mathematical reasoning
References
- [1] "Algebraic Equations" by Math Open Reference
- [2] "Mathematical Puzzles" by Brilliant.org
- [3] "Problem-Solving Techniques" by Khan Academy
Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of resources.