Translate Into An Algebraic Equation And Solve.Sam And Terry Are Going To The Fair. Together, They Have $68 To Spend At The Fair. Sam Has $26. How Much Money Does Terry Have?Provide Your Answer Below:

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Introduction

In this problem, we are given that Sam and Terry have a total of $68 to spend at the fair. We also know that Sam has $26. Our goal is to find out how much money Terry has. To solve this problem, we will use algebraic equations.

Step 1: Define the Variables

Let's define the variables:

  • T = Terry's money
  • S = Sam's money
  • T + S = Total money

We are given that Sam has $26, so we can write:

  • S = 26

Step 2: Write the Equation

We are also given that the total money is $68, so we can write:

  • T + S = 68

Substituting the value of S from Step 1, we get:

  • T + 26 = 68

Step 3: Solve for T

To solve for T, we need to isolate T on one side of the equation. We can do this by subtracting 26 from both sides of the equation:

  • T + 26 - 26 = 68 - 26
  • T = 42

Therefore, Terry has $42.

Conclusion

In this problem, we used algebraic equations to solve for Terry's money at the fair. We defined the variables, wrote the equation, and solved for T. The final answer is $42.

Discussion

This problem is a simple example of how algebraic equations can be used to solve real-world problems. In this case, we used a simple linear equation to solve for Terry's money. However, in more complex problems, we may need to use more advanced algebraic techniques, such as quadratic equations or systems of equations.

Real-World Applications

This problem has many real-world applications. For example, in finance, we may need to solve for the amount of money a person has based on their income and expenses. In business, we may need to solve for the cost of a product based on its price and quantity. In science, we may need to solve for the amount of a substance based on its concentration and volume.

Tips and Tricks

When solving algebraic equations, it's essential to follow the order of operations (PEMDAS):

  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.

By following these steps, you can ensure that you are solving algebraic equations correctly and efficiently.

Practice Problems

Try solving the following problems on your own:

  1. Tom and Alex have a total of $120 to spend at the mall. Tom has $40. How much money does Alex have?
  2. A bakery sells a total of 250 loaves of bread per day. They sell 120 loaves in the morning and 80 loaves in the afternoon. How many loaves do they sell in the evening?
  3. A car travels a total of 240 miles per day. It travels 120 miles in the morning and 80 miles in the afternoon. How many miles does it travel in the evening?

Introduction

In our previous article, we discussed how to solve algebraic equations using simple linear equations. We also provided some real-world applications and tips and tricks for solving these types of equations. In this article, we will answer some frequently asked questions about solving algebraic equations.

Q: What is an algebraic equation?

A: An algebraic equation is a mathematical statement that contains variables and constants. It is a statement that says two expressions are equal, and we need to solve for the value of the variable.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants. A quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, we need to isolate the variable on one side of the equation. We can do this by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides of the equation by the same value.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, we need to use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. This formula will give us two possible values for the variable.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when solving an equation. The order of operations is:

  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 simplify an expression?

A: To simplify an expression, we need to combine like terms. Like terms are terms that have the same variable and exponent. We can combine like terms by adding or subtracting their coefficients.

Q: What is a system of equations?

A: A system of equations is a set of two or more equations that contain the same variables. We need to solve the system of equations to find the values of the variables.

Q: How do I solve a system of equations?

A: To solve a system of equations, we need to use substitution or elimination. Substitution involves solving one equation for one variable and then substituting that value into the other equation. Elimination involves adding or subtracting the equations to eliminate one of the variables.

Q: What is a variable?

A: A variable is a symbol that represents a value that can change. Variables are often represented by letters such as x, y, or z.

Q: What is a constant?

A: A constant is a value that does not change. Constants are often represented by numbers such as 2, 5, or 10.

Conclusion

In this article, we have answered some frequently asked questions about solving algebraic equations. We have discussed the difference between linear and quadratic equations, how to solve these types of equations, and how to simplify expressions. We have also discussed the order of operations and how to solve systems of equations. We hope this article has been helpful in answering your questions about solving algebraic equations.

Practice Problems

Try solving the following problems on your own:

  1. Solve the equation 2x + 5 = 11.
  2. Solve the equation x^2 + 4x + 4 = 0.
  3. Simplify the expression 2x + 3x.
  4. Solve the system of equations x + y = 4 and 2x - 2y = -2.
  5. What is the value of x in the equation x + 2 = 7?

I hope this article has been helpful in answering your questions about solving algebraic equations. Remember to practice regularly and follow the order of operations to ensure that you are solving equations correctly and efficiently.