Jessica's Mom Is 3 Times As Old As Her Daughter.a) Write An Equation To Determine Jessica's Age When Her Mom Is X Years Old.
In this problem, we are given a relationship between Jessica's age and her mother's age. We are told that Jessica's mother is 3 times as old as her daughter. This means that if we let Jessica's age be represented by the variable 'j', then her mother's age can be represented by the expression '3j'. Our goal is to write an equation that determines Jessica's age when her mother is x years old.
Writing the Equation
Let's start by representing Jessica's age as 'j' and her mother's age as '3j'. Since we are given that her mother is x years old, we can set up the equation:
3j = x
This equation represents the relationship between Jessica's age and her mother's age. However, we are asked to determine Jessica's age when her mother is x years old. To do this, we need to isolate the variable 'j' in the equation.
Solving for Jessica's Age
To solve for 'j', we can divide both sides of the equation by 3:
j = x/3
This equation represents Jessica's age in terms of her mother's age. We can now use this equation to determine Jessica's age when her mother is x years old.
Example
Let's say Jessica's mother is 36 years old. We can substitute this value into the equation to determine Jessica's age:
j = 36/3 j = 12
This means that when Jessica's mother is 36 years old, Jessica is 12 years old.
Conclusion
In this problem, we were given a relationship between Jessica's age and her mother's age. We wrote an equation to represent this relationship and solved for Jessica's age in terms of her mother's age. We can use this equation to determine Jessica's age when her mother is x years old.
Real-World Applications
This type of problem has many real-world applications. For example, in finance, we may need to calculate the interest on an investment based on the age of the investor. In medicine, we may need to calculate the dosage of a medication based on the age of the patient. In these cases, we can use equations like the one we derived in this problem to make accurate calculations.
Tips and Tricks
When solving problems like this, it's essential to read the problem carefully and understand the relationship between the variables. In this case, we were given a relationship between Jessica's age and her mother's age, and we used that relationship to write an equation. We then solved for Jessica's age in terms of her mother's age.
Common Mistakes
One common mistake when solving problems like this is to forget to isolate the variable. In this case, we forgot to divide both sides of the equation by 3 to solve for 'j'. This can lead to incorrect answers, so it's essential to double-check our work.
Practice Problems
Here are a few practice problems to help you practice solving equations like the one we derived in this problem:
- If a person's age is 2 times their daughter's age, and the daughter is 8 years old, how old is the person?
- If a person's age is 3 times their son's age, and the son is 12 years old, how old is the person?
- If a person's age is 4 times their daughter's age, and the daughter is 16 years old, how old is the person?
Answer Key
- 16
- 36
- 64
Conclusion
In our previous article, we explored the relationship between Jessica's age and her mother's age. We wrote an equation to represent this relationship and solved for Jessica's age in terms of her mother's age. In this article, we will answer some frequently asked questions about this problem.
Q: What is the relationship between Jessica's age and her mother's age?
A: The relationship between Jessica's age and her mother's age is that her mother is 3 times as old as her daughter. This means that if we let Jessica's age be represented by the variable 'j', then her mother's age can be represented by the expression '3j'.
Q: How do I write an equation to represent this relationship?
A: To write an equation to represent this relationship, we can use the expression '3j' to represent her mother's age. We can then set up the equation:
3j = x
This equation represents the relationship between Jessica's age and her mother's age.
Q: How do I solve for Jessica's age in terms of her mother's age?
A: To solve for Jessica's age in terms of her mother's age, we can divide both sides of the equation by 3:
j = x/3
This equation represents Jessica's age in terms of her mother's age.
Q: What if I want to find Jessica's age when her mother is 36 years old?
A: To find Jessica's age when her mother is 36 years old, we can substitute this value into the equation:
j = 36/3 j = 12
This means that when Jessica's mother is 36 years old, Jessica is 12 years old.
Q: Can I use this equation to find Jessica's age when her mother is any age?
A: Yes, you can use this equation to find Jessica's age when her mother is any age. Simply substitute the value of her mother's age into the equation, and you will get Jessica's age.
Q: What if I want to find the age of Jessica's mother when Jessica is 12 years old?
A: To find the age of Jessica's mother when Jessica is 12 years old, we can substitute this value into the equation:
3j = x 3(12) = x 36 = x
This means that when Jessica is 12 years old, her mother is 36 years old.
Q: Can I use this equation to find the age of Jessica's mother when Jessica is any age?
A: Yes, you can use this equation to find the age of Jessica's mother when Jessica is any age. Simply substitute the value of Jessica's age into the equation, and you will get the age of her mother.
Q: What if I want to find the age of Jessica's mother when she is 3 times as old as Jessica?
A: To find the age of Jessica's mother when she is 3 times as old as Jessica, we can set up the equation:
3j = x
This equation represents the relationship between Jessica's age and her mother's age. We can then solve for x to find the age of her mother.
Q: Can I use this equation to find the age of Jessica's mother when she is any multiple of Jessica's age?
A: Yes, you can use this equation to find the age of Jessica's mother when she is any multiple of Jessica's age. Simply substitute the multiple into the equation, and you will get the age of her mother.
Conclusion
In this article, we answered some frequently asked questions about the relationship between Jessica's age and her mother's age. We wrote an equation to represent this relationship and solved for Jessica's age in terms of her mother's age. We can use this equation to find Jessica's age when her mother is any age, and we can also use it to find the age of her mother when Jessica is any age.