Beverly Has A Bag Of Marbles That Weighs 30 Grams. She Knows That Each Marble Weighs 1.5 Grams And The Bag Itself Weighs 1.5 Grams.Which Equation Could She Use To Determine How Many Marbles Are In The Bag? Select All That Apply.A. [$(1.5) X + 1.5
Introduction
In this article, we will delve into the world of mathematics and explore a real-life scenario involving marbles and their weights. Beverly has a bag of marbles that weighs 30 grams, and she wants to determine how many marbles are in the bag. Each marble weighs 1.5 grams, and the bag itself weighs 1.5 grams. We will examine the equation that Beverly can use to solve this problem.
Understanding the Problem
To solve this problem, we need to understand the relationship between the weight of the marbles, the weight of the bag, and the total weight of the marbles and the bag. Let's denote the number of marbles as x. The weight of each marble is 1.5 grams, so the total weight of the marbles is 1.5x grams. The weight of the bag is 1.5 grams, so the total weight of the marbles and the bag is 1.5x + 1.5 grams.
The Equation
The equation that Beverly can use to determine the number of marbles in the bag is:
1.5x + 1.5 = 30
This equation represents the total weight of the marbles and the bag, which is equal to 30 grams.
Solving the Equation
To solve the equation, we need to isolate the variable x. We can do this by subtracting 1.5 from both sides of the equation:
1.5x = 30 - 1.5 1.5x = 28.5
Next, we can divide both sides of the equation by 1.5 to solve for x:
x = 28.5 / 1.5 x = 19
Therefore, there are 19 marbles in the bag.
Alternative Equations
In addition to the equation 1.5x + 1.5 = 30, there are other equations that Beverly can use to solve this problem. These equations are:
- 1.5x = 30 - 1.5
- 1.5x - 1.5 = 30
- 1.5x + 1.5 - 1.5 = 30
- 1.5x = 30 - 1.5 + 1.5
These equations are equivalent to the original equation and can be used to solve for x.
Conclusion
In conclusion, the equation that Beverly can use to determine the number of marbles in the bag is 1.5x + 1.5 = 30. By solving this equation, we can find the value of x, which represents the number of marbles in the bag. This problem is a great example of how mathematics can be used to solve real-life problems.
Mathematical Concepts
This problem involves several mathematical concepts, including:
- Algebra: The equation 1.5x + 1.5 = 30 is an example of a linear equation, which is a fundamental concept in algebra.
- Equations: The equation 1.5x + 1.5 = 30 is an example of a linear equation, which is a type of equation that can be solved using algebraic methods.
- Variables: The variable x represents the number of marbles in the bag, and its value can be found by solving the equation.
- Constants: The constants 1.5 and 30 are used in the equation to represent the weight of the marbles and the bag, respectively.
Real-World Applications
This problem has several real-world applications, including:
- Science: The concept of weight and mass is fundamental to science, and this problem demonstrates how to use mathematical equations to solve problems involving weight and mass.
- Engineering: The concept of weight and mass is also important in engineering, where it is used to design and build structures and machines.
- Business: The concept of weight and mass is also used in business, where it is used to calculate the cost of goods and services.
Final Thoughts
Q: What is the weight of each marble in the bag?
A: The weight of each marble in the bag is 1.5 grams.
Q: What is the weight of the bag itself?
A: The weight of the bag itself is 1.5 grams.
Q: What is the total weight of the marbles and the bag?
A: The total weight of the marbles and the bag is 30 grams.
Q: How can I solve the equation 1.5x + 1.5 = 30 to find the number of marbles in the bag?
A: To solve the equation 1.5x + 1.5 = 30, you can follow these steps:
- Subtract 1.5 from both sides of the equation: 1.5x = 30 - 1.5
- Simplify the right-hand side of the equation: 1.5x = 28.5
- Divide both sides of the equation by 1.5: x = 28.5 / 1.5
- Simplify the right-hand side of the equation: x = 19
Q: What is the value of x in the equation 1.5x + 1.5 = 30?
A: The value of x in the equation 1.5x + 1.5 = 30 is 19.
Q: Can I use other equations to solve for x?
A: Yes, you can use other equations to solve for x. Some examples include:
- 1.5x = 30 - 1.5
- 1.5x - 1.5 = 30
- 1.5x + 1.5 - 1.5 = 30
- 1.5x = 30 - 1.5 + 1.5
Q: What are some real-world applications of the equation 1.5x + 1.5 = 30?
A: Some real-world applications of the equation 1.5x + 1.5 = 30 include:
- Science: The concept of weight and mass is fundamental to science, and this equation demonstrates how to use mathematical equations to solve problems involving weight and mass.
- Engineering: The concept of weight and mass is also important in engineering, where it is used to design and build structures and machines.
- Business: The concept of weight and mass is also used in business, where it is used to calculate the cost of goods and services.
Q: What mathematical concepts are involved in solving the equation 1.5x + 1.5 = 30?
A: The mathematical concepts involved in solving the equation 1.5x + 1.5 = 30 include:
- Algebra: The equation 1.5x + 1.5 = 30 is an example of a linear equation, which is a fundamental concept in algebra.
- Equations: The equation 1.5x + 1.5 = 30 is an example of a linear equation, which is a type of equation that can be solved using algebraic methods.
- Variables: The variable x represents the number of marbles in the bag, and its value can be found by solving the equation.
- Constants: The constants 1.5 and 30 are used in the equation to represent the weight of the marbles and the bag, respectively.
Q: Can I use this equation to solve other problems involving weight and mass?
A: Yes, you can use this equation to solve other problems involving weight and mass. Simply substitute the values of the variables and constants into the equation and solve for the unknown variable.