At Practice, Diego Completed Twice As Many Push-ups As Noah. Diego Also Completed 40 Jumping Jacks. He Completed 62 Push-ups And Jumping Jacks Altogether. The Equation $2x + 40 = 62$ Represents This Situation. What Does The Variable

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Solving the Equation: Unraveling the Mystery of Diego's Workout

In the world of mathematics, equations are used to represent real-world situations. They help us understand and solve problems by breaking them down into manageable parts. In this article, we will delve into the world of algebra and explore how to solve a simple equation that represents a real-life scenario. We will use the equation 2x+40=622x + 40 = 62 to understand the relationship between Diego's push-ups and jumping jacks.

The equation 2x+40=622x + 40 = 62 represents the situation where Diego completed twice as many push-ups as Noah and also completed 40 jumping jacks. The equation can be broken down into two parts:

  • 2x2x represents the number of push-ups Diego completed.
  • 4040 represents the number of jumping jacks Diego completed.
  • 6262 represents the total number of push-ups and jumping jacks Diego completed.

To solve for the variable xx, we need to isolate it on one side of the equation. We can do this by subtracting 4040 from both sides of the equation:

2x+40−40=62−402x + 40 - 40 = 62 - 40

This simplifies to:

2x=222x = 22

Next, we need to divide both sides of the equation by 22 to solve for xx:

2x2=222\frac{2x}{2} = \frac{22}{2}

This simplifies to:

x=11x = 11

So, what does the variable xx represent? In this case, xx represents the number of push-ups Diego completed. Since Diego completed twice as many push-ups as Noah, we can conclude that Noah completed half the number of push-ups that Diego completed. Therefore, Noah completed 11÷2=5.511 \div 2 = 5.5 push-ups.

In conclusion, we have solved the equation 2x+40=622x + 40 = 62 to find the value of the variable xx. We have also interpreted the result to understand the relationship between Diego's push-ups and jumping jacks. This equation represents a real-life scenario where Diego completed twice as many push-ups as Noah and also completed 40 jumping jacks. By solving the equation, we have gained insight into the number of push-ups Diego completed and the number of push-ups Noah completed.

This equation has real-world applications in various fields such as:

  • Sports: In sports, equations like this can be used to track an athlete's performance and set goals for improvement.
  • Business: In business, equations like this can be used to model sales and revenue growth.
  • Science: In science, equations like this can be used to model population growth and predict future trends.

Here are some tips and tricks to help you solve equations like this:

  • Read the equation carefully: Before solving the equation, read it carefully to understand what it represents.
  • Identify the variable: Identify the variable you need to solve for and isolate it on one side of the equation.
  • Use inverse operations: Use inverse operations to solve for the variable. For example, if you have a multiplication operation, use division to solve for the variable.
  • Check your answer: Once you have solved for the variable, check your answer to make sure it makes sense in the context of the problem.

Here are some common mistakes to avoid when solving equations like this:

  • Not reading the equation carefully: Failing to read the equation carefully can lead to misunderstandings and incorrect solutions.
  • Not identifying the variable: Failing to identify the variable can lead to incorrect solutions.
  • Not using inverse operations: Failing to use inverse operations can lead to incorrect solutions.
  • Not checking your answer: Failing to check your answer can lead to incorrect solutions.

In conclusion, solving the equation 2x+40=622x + 40 = 62 has given us insight into the number of push-ups Diego completed and the number of push-ups Noah completed. This equation represents a real-life scenario where Diego completed twice as many push-ups as Noah and also completed 40 jumping jacks. By following the steps outlined in this article, you can solve equations like this and gain a deeper understanding of the world around you.
Frequently Asked Questions: Solving the Equation

A: The equation 2x+40=622x + 40 = 62 is trying to represent the situation where Diego completed twice as many push-ups as Noah and also completed 40 jumping jacks.

A: The variable xx represents the number of push-ups Diego completed.

A: To solve for the variable xx, you need to isolate it on one side of the equation. You can do this by subtracting 40 from both sides of the equation and then dividing both sides by 2.

A: The value of the variable xx in the equation is 11.

A: The value of the variable xx represents the number of push-ups Diego completed. Since Diego completed twice as many push-ups as Noah, we can conclude that Noah completed half the number of push-ups that Diego completed.

A: You can apply the concept of solving equations to real-world problems by using equations to model real-world situations. For example, you can use equations to track an athlete's performance, model sales and revenue growth, or predict population growth.

A: Some common mistakes to avoid when solving equations include not reading the equation carefully, not identifying the variable, not using inverse operations, and not checking your answer.

A: You can check your answer by plugging it back into the original equation and making sure it is true. You can also use your common sense and check if the answer makes sense in the context of the problem.

A: Some real-world applications of solving equations include:

  • Sports: In sports, equations can be used to track an athlete's performance and set goals for improvement.
  • Business: In business, equations can be used to model sales and revenue growth.
  • Science: In science, equations can be used to model population growth and predict future trends.

A: You can improve your skills in solving equations by practicing regularly, reading math books and articles, and working with a tutor or mentor. You can also try solving equations in different contexts, such as sports, business, and science, to see how they apply to real-world problems.

In conclusion, solving the equation 2x+40=622x + 40 = 62 has given us insight into the number of push-ups Diego completed and the number of push-ups Noah completed. This equation represents a real-life scenario where Diego completed twice as many push-ups as Noah and also completed 40 jumping jacks. By following the steps outlined in this article and practicing regularly, you can improve your skills in solving equations and apply them to real-world problems.