Marta Runs A Mandarin-orange Fruit Stand. She Is Talking To An Employee, Maribel, On The Phone And Trying To Tell Her The Equation Needed To Figure Out How Many Oranges To Send To A Certain Customer.The Equation Is $50+\frac{1}{2} M=120$.
Introduction
Marta, the owner of a popular mandarin-orange fruit stand, is on the phone with her employee, Maribel, discussing the equation needed to determine the number of oranges to send to a specific customer. The equation, $50+\frac{1}{2} m=120$, requires Maribel to solve for the variable 'm', which represents the number of oranges to be sent. In this article, we will guide Maribel through the step-by-step process of solving the equation and provide a clear understanding of the mathematical concepts involved.
Understanding the Equation
The given equation is a linear equation in the form of $ax + b = c$, where 'a' is the coefficient of the variable 'x', 'b' is the constant term, and 'c' is the constant on the right-hand side of the equation. In this case, the equation is $50+\frac{1}{2} m=120$, where 'm' is the variable we need to solve for.
Step 1: Isolate the Variable Term
To solve for 'm', we need to isolate the variable term on one side of the equation. The first step is to subtract 50 from both sides of the equation, which will eliminate the constant term on the left-hand side.
Subtract 50 from both sides:
Step 2: Multiply Both Sides by the Reciprocal of the Coefficient
The next step is to multiply both sides of the equation by the reciprocal of the coefficient of the variable term. In this case, the coefficient of 'm' is , so we need to multiply both sides by 2 to eliminate the fraction.
Multiply both sides by 2:
Conclusion
By following the step-by-step process outlined above, Maribel can solve the equation $50+\frac{1}{2} m=120$ and determine the number of oranges to send to the customer. The solution to the equation is , which means that Maribel should send 140 oranges to the customer.
Real-World Applications
The equation $50+\frac{1}{2} m=120$ has real-world applications in various fields, including business, economics, and science. For example, in business, the equation can be used to determine the number of products to produce and sell based on a given demand. In economics, the equation can be used to model the supply and demand of a particular good or service. In science, the equation can be used to model the growth and decay of populations.
Tips and Tricks
When solving linear equations, it's essential to follow the order of operations (PEMDAS) and to isolate the variable term on one side of the equation. Additionally, when working with fractions, it's helpful to multiply both sides of the equation by the reciprocal of the coefficient to eliminate the fraction.
Common Mistakes
When solving linear equations, some common mistakes to avoid include:
- Not following the order of operations (PEMDAS)
- Not isolating the variable term on one side of the equation
- Not multiplying both sides of the equation by the reciprocal of the coefficient when working with fractions
Final Thoughts
Introduction
In our previous article, we guided Maribel, the employee of a popular mandarin-orange fruit stand, through the step-by-step process of solving the equation $50+\frac{1}{2} m=120$. In this article, we will address some common questions and concerns that Maribel may have had while solving the equation.
Q: What is the first step in solving a linear equation?
A: The first step in solving a linear equation is to isolate the variable term on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Q: How do I know which operation to perform first?
A: To determine which operation to perform first, you should follow the order of operations (PEMDAS):
- Parentheses: Evaluate any 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.
Q: What is the reciprocal of a fraction?
A: The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, the reciprocal of is .
Q: Why do I need to multiply both sides of the equation by the reciprocal of the coefficient?
A: When working with fractions, it's essential to multiply both sides of the equation by the reciprocal of the coefficient to eliminate the fraction. This is because multiplying both sides of the equation by the reciprocal of the coefficient is equivalent to multiplying both sides by 1, which does not change the value of the equation.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable is 1. For example, the equation $2x + 3 = 5$ is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation.
Q: How do I know if an equation is linear or quadratic?
A: To determine if an equation is linear or quadratic, you should look at the highest power of the variable. If the highest power of the variable is 1, the equation is linear. If the highest power of the variable is 2, the equation is quadratic.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not following the order of operations (PEMDAS)
- Not isolating the variable term on one side of the equation
- Not multiplying both sides of the equation by the reciprocal of the coefficient when working with fractions
Conclusion
Solving linear equations is a fundamental skill in mathematics that has real-world applications in various fields. By following the step-by-step process outlined above and addressing common questions and concerns, Maribel can become a more confident and proficient problem-solver. Additionally, by understanding the mathematical concepts involved, Maribel can apply this skill to other real-world problems and become a more effective and efficient problem-solver.
Tips and Tricks
When solving linear equations, it's essential to follow the order of operations (PEMDAS) and to isolate the variable term on one side of the equation. Additionally, when working with fractions, it's helpful to multiply both sides of the equation by the reciprocal of the coefficient to eliminate the fraction.
Common Mistakes
When solving linear equations, some common mistakes to avoid include:
- Not following the order of operations (PEMDAS)
- Not isolating the variable term on one side of the equation
- Not multiplying both sides of the equation by the reciprocal of the coefficient when working with fractions
Final Thoughts
Solving linear equations is a fundamental skill in mathematics that has real-world applications in various fields. By following the step-by-step process outlined above and addressing common questions and concerns, Maribel can become a more confident and proficient problem-solver. Additionally, by understanding the mathematical concepts involved, Maribel can apply this skill to other real-world problems and become a more effective and efficient problem-solver.