Select The Correct Answer.During The Summer, Jody Earns $10 Per Hour Babysitting And $15 Per Hour Doing Yard Work. This Week She Worked A Total Of 34 Hours. If { X $}$ Represents The Number Of Hours She Babysat And [$ Y
Introduction
In this article, we will explore a math problem involving Jody's summer earnings from babysitting and yard work. We will use algebraic equations to represent the given information and solve for the number of hours Jody spent babysitting and doing yard work.
The Problem
Jody earns $10 per hour babysitting and $15 per hour doing yard work. This week, she worked a total of 34 hours. If x represents the number of hours she babysat and y represents the number of hours she did yard work, we can write the following equation:
10x + 15y = 34
Understanding the Equation
The equation 10x + 15y = 34 represents the total earnings from babysitting and yard work. The left-hand side of the equation is the sum of the earnings from babysitting (10x) and yard work (15y). The right-hand side of the equation is the total earnings, which is $34.
Solving the Equation
To solve the equation, we need to find the values of x and y that satisfy the equation. We can start by isolating one of the variables. Let's isolate x by subtracting 15y from both sides of the equation:
10x = 34 - 15y
Now, we can divide both sides of the equation by 10 to solve for x:
x = (34 - 15y) / 10
Substituting x into the Original Equation
Now that we have an expression for x, we can substitute it into the original equation:
10((34 - 15y) / 10) + 15y = 34
Simplifying the equation, we get:
34 - 15y + 15y = 34
The y terms cancel out, and we are left with:
34 = 34
This equation is true for all values of y, which means that y can be any number. However, we know that Jody worked a total of 34 hours, so we can set up an equation to represent this:
x + y = 34
Substituting x into the Equation
Now that we have an expression for x, we can substitute it into the equation:
((34 - 15y) / 10) + y = 34
Multiplying both sides of the equation by 10 to eliminate the fraction, we get:
34 - 15y + 10y = 340
Simplifying the equation, we get:
34 - 5y = 340
Subtracting 34 from both sides of the equation, we get:
-5y = 306
Dividing both sides of the equation by -5, we get:
y = -306 / 5
y = -61.2
Finding the Value of x
Now that we have the value of y, we can substitute it into the equation x + y = 34 to find the value of x:
x + (-61.2) = 34
Adding 61.2 to both sides of the equation, we get:
x = 34 + 61.2
x = 95.2
Conclusion
In this article, we solved a math problem involving Jody's summer earnings from babysitting and yard work. We used algebraic equations to represent the given information and solve for the number of hours Jody spent babysitting and doing yard work. We found that Jody spent 95.2 hours babysitting and 61.2 hours doing yard work.
Key Takeaways
- Algebraic equations can be used to represent real-world problems.
- Solving equations can help us find the values of variables that satisfy the equation.
- In this problem, we used substitution to solve for the value of x and then found the value of y.
Real-World Applications
This problem has real-world applications in various fields, such as:
- Business: Understanding how to calculate earnings and expenses is crucial for businesses to make informed decisions.
- Finance: Calculating earnings and expenses is essential for individuals and businesses to manage their finances effectively.
- Science: Algebraic equations are used to model real-world phenomena, such as population growth and chemical reactions.
Final Thoughts
Introduction
In our previous article, we explored a math problem involving Jody's summer earnings from babysitting and yard work. We used algebraic equations to represent the given information and solve for the number of hours Jody spent babysitting and doing yard work. In this article, we will answer some frequently asked questions related to the problem.
Q&A
Q: What is the total earnings from babysitting and yard work?
A: The total earnings from babysitting and yard work is $34.
Q: How many hours did Jody spend babysitting?
A: Jody spent 95.2 hours babysitting.
Q: How many hours did Jody spend doing yard work?
A: Jody spent 61.2 hours doing yard work.
Q: What is the equation that represents the total earnings from babysitting and yard work?
A: The equation that represents the total earnings from babysitting and yard work is 10x + 15y = 34.
Q: How did you solve the equation?
A: We solved the equation by isolating one of the variables, x, and then substituting it into the original equation.
Q: What is the value of x in terms of y?
A: The value of x in terms of y is x = (34 - 15y) / 10.
Q: Can you explain the concept of substitution in solving equations?
A: Substitution is a technique used to solve equations by substituting an expression for one variable into the equation. In this problem, we substituted the expression for x into the original equation to solve for y.
Q: What are some real-world applications of algebraic equations?
A: Algebraic equations have many real-world applications, including business, finance, and science. They can be used to model real-world phenomena, such as population growth and chemical reactions.
Q: How can algebraic equations be used in business?
A: Algebraic equations can be used in business to calculate earnings and expenses, model sales and revenue, and make informed decisions.
Q: How can algebraic equations be used in finance?
A: Algebraic equations can be used in finance to calculate interest rates, model investment returns, and make informed investment decisions.
Q: How can algebraic equations be used in science?
A: Algebraic equations can be used in science to model real-world phenomena, such as population growth and chemical reactions.
Conclusion
In this article, we answered some frequently asked questions related to the math problem involving Jody's summer earnings from babysitting and yard work. We hope that this Q&A article has provided a better understanding of the problem and its solutions.
Key Takeaways
- Algebraic equations can be used to represent real-world problems.
- Substitution is a technique used to solve equations by substituting an expression for one variable into the equation.
- Algebraic equations have many real-world applications, including business, finance, and science.
Real-World Applications
This problem has real-world applications in various fields, such as:
- Business: Understanding how to calculate earnings and expenses is crucial for businesses to make informed decisions.
- Finance: Calculating earnings and expenses is essential for individuals and businesses to manage their finances effectively.
- Science: Algebraic equations are used to model real-world phenomena, such as population growth and chemical reactions.
Final Thoughts
In conclusion, this Q&A article has provided a better understanding of the math problem involving Jody's summer earnings from babysitting and yard work. We hope that this article has been helpful in answering some of the frequently asked questions related to the problem.