Form An Equation From The Word Problem. Solve To Answer The Question.A Number Is 2 3 \frac{2}{3} 3 2 ​ Of Another Number. If The Sum Of The Two Numbers Is 30, Find The Smaller Number. (Let The Other Number Be X X X .)A. X = − 9 X = -9 X = − 9 B.

Introduction

Word problems are an essential part of mathematics, and forming equations from them is a crucial skill that students need to master. In this article, we will learn how to form an equation from a word problem and solve it to answer the question. We will use a specific example to illustrate the process.

Understanding the Problem

The problem states that a number is $\frac{2}{3}$ of another number. If the sum of the two numbers is 30, find the smaller number. Let's denote the other number as $x$. Our goal is to find the value of $x$.

Forming the Equation

To form the equation, we need to translate the word problem into a mathematical expression. We know that the number is $\frac{2}{3}$ of $x$, so we can write an equation:

$$\frac{2}{3}x + x = 30$$

This equation represents the sum of the two numbers, which is equal to 30.

Solving the Equation

To solve the equation, we need to isolate the variable $x$. We can start by combining the two terms on the left-hand side:

$$\frac{2}{3}x + x = \frac{5}{3}x$$

Now, we can rewrite the equation as:

$$\frac{5}{3}x = 30$$

To solve for $x$, we need to multiply both sides of the equation by the reciprocal of $\frac{5}{3}$, which is $\frac{3}{5}$:

$$x = 30 \times \frac{3}{5}$$

Simplifying the expression, we get:

$$x = 18$$

Conclusion

In this article, we learned how to form an equation from a word problem and solve it to answer the question. We used a specific example to illustrate the process, and we found that the value of $x$ is 18.

Tips and Tricks

• When forming an equation from a word problem, make sure to read the problem carefully and identify the key information.
• Use variables to represent the unknown quantities in the problem.
• Translate the word problem into a mathematical expression, using algebraic operations such as addition, subtraction, multiplication, and division.
• Solve the equation by isolating the variable and using inverse operations.

Practice Problems

Try forming equations from the following word problems and solving them to answer the questions:

1. A car travels 250 miles in 5 hours. If the car travels at a constant speed, how many miles does it travel in 1 hour?
2. A bakery sells 500 loaves of bread per day. If each loaf costs $2, how much money does the bakery make in a day?
3. A group of friends want to share some candy equally. If they have 48 pieces of candy and there are 8 friends, how many pieces of candy will each friend get?

Answer Key

1. 50 miles per hour
2. $1000
3. 6 pieces of candy per friend

Discussion

What are some common challenges that students face when forming equations from word problems? How can teachers and educators help students overcome these challenges?

Conclusion

Introduction

Forming equations from word problems is a crucial skill that students need to master. In our previous article, we learned how to form an equation from a word problem and solve it to answer the question. In this article, we will answer some frequently asked questions about forming equations from word problems.

Q: What is the first step in forming an equation from a word problem?

A: The first step in forming an equation from a word problem is to read the problem carefully and identify the key information. This includes understanding the problem, identifying the variables, and determining the relationships between the variables.

Q: How do I know which variable to use as the subject of the equation?

A: When forming an equation from a word problem, you need to identify the variable that is being asked about. This is usually the variable that is being solved for. For example, if the problem asks for the value of x, then x is the subject of the equation.

Q: What is the difference between a variable and a constant?

A: A variable is a value that can change, while a constant is a value that remains the same. In an equation, variables are represented by letters, such as x or y, while constants are represented by numbers.

Q: How do I know which operation to use when forming an equation from a word problem?

A: When forming an equation from a word problem, you need to use the operations that are described in the problem. For example, if the problem states that a number is increased by 5, then you would use the addition operation.

Q: What is the order of operations when forming an equation from a word problem?

A: The order of operations when forming an equation from a word problem is the same as the order of operations in algebra:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I know if an equation is true or false?

A: To determine if an equation is true or false, you need to substitute the values of the variables into the equation and evaluate the expression. If the expression is equal to the value on the right-hand side of the equation, then the equation is true. Otherwise, the equation is false.

Q: What are some common mistakes to avoid when forming equations from word problems?

A: Some common mistakes to avoid when forming equations from word problems include:

• Not reading the problem carefully and identifying the key information.
• Not using the correct variables and constants.
• Not using the correct operations.
• Not following the order of operations.

Q: How can I practice forming equations from word problems?

A: There are many ways to practice forming equations from word problems, including:

• Working through practice problems in a textbook or online resource.
• Creating your own word problems and forming equations from them.
• Solving real-world problems that involve forming equations from word problems.

Conclusion

Forming equations from word problems is a crucial skill that students need to master. By following the steps outlined in this article and practicing regularly, students can become proficient in forming equations from word problems and solving them to answer the questions.

Additional Resources

• Mathway: A online math problem solver that can help you form equations from word problems.
• Khan Academy: A free online resource that offers video lessons and practice problems on forming equations from word problems.
• Math Open Reference: A free online reference book that offers information and examples on forming equations from word problems.

Discussion

What are some common challenges that students face when forming equations from word problems? How can teachers and educators help students overcome these challenges?

Conclusion

Forming equations from word problems is a crucial skill that students need to master. By following the steps outlined in this article and practicing regularly, students can become proficient in forming equations from word problems and solving them to answer the questions.