Molly Has $4x + 10$ Dollars, And Ron Has $20 - 5x$ Dollars.a. How Much Money Do They Have Altogether?b. Simplify The Expression: ${ 4x - 5x + 10 + 20 = -1x + 30 }$

In this article, we will delve into the world of mathematics and explore how to combine money using algebraic expressions. We will examine a scenario where Molly has a certain amount of money, and Ron has a different amount of money. Our goal is to determine the total amount of money they have altogether.

Understanding the Problem

Molly has $4x + 10$ dollars, and Ron has $20 - 5x$ dollars. To find the total amount of money they have, we need to combine these two expressions.

Step 1: Combining Like Terms

To combine the expressions, we need to simplify the equation by combining like terms. Like terms are terms that have the same variable raised to the same power.

(4x + 10) + (20 - 5x)

We can start by combining the like terms:

• The terms with the variable $x$ are $4x$ and $-5x$. We can combine these terms by adding their coefficients: $4x - 5x = -1x$.
• The constant terms are $10$ and $20$. We can combine these terms by adding them: $10 + 20 = 30$.

Step 2: Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression:

-1x + 30

This is the simplified expression.

Discussion

In this problem, we used algebraic expressions to represent the amount of money Molly and Ron have. We combined these expressions by simplifying the equation and combining like terms. This is an important concept in mathematics, as it allows us to solve problems involving variables and unknown values.

Real-World Applications

This problem has real-world applications in finance and economics. For example, if we were to represent the amount of money in a bank account using an algebraic expression, we could use the same techniques to combine the expressions and determine the total amount of money in the account.

Conclusion

In conclusion, combining money using algebraic expressions is an important concept in mathematics. By simplifying the equation and combining like terms, we can determine the total amount of money two people have. This problem has real-world applications in finance and economics, and is an important tool for solving problems involving variables and unknown values.

Additional Examples

Here are a few additional examples of combining money using algebraic expressions:

• If Molly has $2x + 15$ dollars and Ron has $10 - 3x$ dollars, how much money do they have altogether?
• If Molly has $5x - 2$ dollars and Ron has $8 + 2x$ dollars, how much money do they have altogether?

These problems can be solved using the same techniques as the original problem.

Solutions

Here are the solutions to the additional examples:

• If Molly has $2x + 15$ dollars and Ron has $10 - 3x$ dollars, we can combine the expressions by simplifying the equation and combining like terms:

(2x + 15) + (10 - 3x)

We can start by combining the like terms:

• The terms with the variable $x$ are $2x$ and $-3x$. We can combine these terms by adding their coefficients: $2x - 3x = -1x$.
• The constant terms are $15$ and $10$. We can combine these terms by adding them: $15 + 10 = 25$.

The simplified expression is:

-1x + 25

• If Molly has $5x - 2$ dollars and Ron has $8 + 2x$ dollars, we can combine the expressions by simplifying the equation and combining like terms:

(5x - 2) + (8 + 2x)

We can start by combining the like terms:

• The terms with the variable $x$ are $5x$ and $2x$. We can combine these terms by adding their coefficients: $5x + 2x = 7x$.
• The constant terms are $-2$ and $8$. We can combine these terms by adding them: $-2 + 8 = 6$.

The simplified expression is:

7x + 6

Conclusion

Q&A: Combining Money Using Algebraic Expressions

In this article, we will continue to explore the concept of combining money using algebraic expressions. We will answer some common questions and provide additional examples to help you understand this important concept in mathematics.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms and simplifying an expression are two related but distinct concepts in mathematics.

• Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.
• Simplifying an expression involves rewriting the expression in a simpler form, often by combining like terms.

Q: How do I know which terms to combine?

A: To determine which terms to combine, look for terms that have the same variable raised to the same power. These are the like terms.

Q: What if I have a term with a negative coefficient?

A: If you have a term with a negative coefficient, you can still combine it with other like terms. For example:

-3x + 2x

You can combine the like terms by adding their coefficients:

-3x + 2x = -1x

Q: Can I combine terms with different variables?

A: No, you cannot combine terms with different variables. For example:

2x + 3y

You cannot combine the like terms because they have different variables.

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, look for like terms and combine them. For example:

2x + 3y + 4x - 2y

You can combine the like terms by adding their coefficients:

(2x + 4x) + (3y - 2y)

6x + y

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions. To do this, look for like terms and combine them. For example:

2/3x + 1/3x

You can combine the like terms by adding their coefficients:

(2/3x + 1/3x) = 3/3x

x

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms left to combine. For example:

2x + 3y

This expression is not simplified because there are like terms left to combine.

Q: Can I simplify an expression with parentheses?

A: Yes, you can simplify an expression with parentheses. To do this, look for like terms and combine them inside the parentheses. For example:

(2x + 3y) + (4x - 2y)

You can combine the like terms inside the parentheses:

(2x + 4x) + (3y - 2y)

6x + y

Conclusion

In conclusion, combining money using algebraic expressions is an important concept in mathematics. By simplifying the equation and combining like terms, we can determine the total amount of money two people have. This problem has real-world applications in finance and economics, and is an important tool for solving problems involving variables and unknown values.

Additional Examples

Here are a few additional examples of combining money using algebraic expressions:

• If Molly has $2x + 15$ dollars and Ron has $10 - 3x$ dollars, how much money do they have altogether?
• If Molly has $5x - 2$ dollars and Ron has $8 + 2x$ dollars, how much money do they have altogether?

These problems can be solved using the same techniques as the original problem.

Solutions

Here are the solutions to the additional examples:

• If Molly has $2x + 15$ dollars and Ron has $10 - 3x$ dollars, we can combine the expressions by simplifying the equation and combining like terms:

(2x + 15) + (10 - 3x)

We can start by combining the like terms:

• The terms with the variable $x$ are $2x$ and $-3x$. We can combine these terms by adding their coefficients: $2x - 3x = -1x$.
• The constant terms are $15$ and $10$. We can combine these terms by adding them: $15 + 10 = 25$.

The simplified expression is:

-1x + 25

• If Molly has $5x - 2$ dollars and Ron has $8 + 2x$ dollars, we can combine the expressions by simplifying the equation and combining like terms:

(5x - 2) + (8 + 2x)

We can start by combining the like terms:

• The terms with the variable $x$ are $5x$ and $2x$. We can combine these terms by adding their coefficients: $5x + 2x = 7x$.
• The constant terms are $-2$ and $8$. We can combine these terms by adding them: $-2 + 8 = 6$.

The simplified expression is:

7x + 6

Conclusion

In conclusion, combining money using algebraic expressions is an important concept in mathematics. By simplifying the equation and combining like terms, we can determine the total amount of money two people have. This problem has real-world applications in finance and economics, and is an important tool for solving problems involving variables and unknown values.