The Total Cost Of 10 Pens And 7 Copies Is Rs. 550. If The Cost Of One Pen Is Rs. 10 Less Than The Cost Of A Copy, Then:a. Express The Situation As A Linear Equation.b. Find The Cost Of A Pen And A Copy.

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Introduction

In this discussion, we will explore a real-world scenario involving the cost of pens and copies. We will express the situation as a linear equation and then solve for the cost of a pen and a copy. This problem is a great example of how linear equations can be used to model real-world situations.

Expressing the Situation as a Linear Equation

Let's denote the cost of a pen as x and the cost of a copy as y. We are given that the total cost of 10 pens and 7 copies is Rs. 550. We can express this situation as a linear equation:

10x + 7y = 550

We are also given that the cost of one pen is Rs. 10 less than the cost of a copy. This can be expressed as:

x = y - 10

Substituting the Second Equation into the First Equation

We can substitute the second equation into the first equation to get:

10(y - 10) + 7y = 550

Expanding the equation, we get:

10y - 100 + 7y = 550

Combine like terms:

17y - 100 = 550

Add 100 to both sides:

17y = 650

Divide both sides by 17:

y = 38.24

Finding the Cost of a Pen

Now that we have found the cost of a copy, we can find the cost of a pen by substituting the value of y into the second equation:

x = y - 10 x = 38.24 - 10 x = 28.24

Conclusion

In this discussion, we expressed the situation involving the cost of pens and copies as a linear equation and then solved for the cost of a pen and a copy. We found that the cost of a copy is Rs. 38.24 and the cost of a pen is Rs. 28.24. This problem is a great example of how linear equations can be used to model real-world situations.

Key Takeaways

  • We can express real-world situations as linear equations.
  • We can use substitution to solve linear equations.
  • We can use linear equations to model real-world situations involving multiple variables.

Real-World Applications

This problem has many real-world applications, such as:

  • Business: A company that sells pens and copies can use linear equations to determine the cost of each item and make informed business decisions.
  • Finance: A financial analyst can use linear equations to model the cost of different financial instruments and make investment decisions.
  • Science: A scientist can use linear equations to model the behavior of physical systems and make predictions about future behavior.

Common Mistakes

  • Not expressing the situation as a linear equation: Failing to express the situation as a linear equation can make it difficult to solve the problem.
  • Not using substitution: Failing to use substitution can make it difficult to solve the problem.
  • Not checking units: Failing to check units can lead to incorrect solutions.

Conclusion

Q: What is the total cost of 10 pens and 7 copies?

A: The total cost of 10 pens and 7 copies is Rs. 550.

Q: How can we express the situation as a linear equation?

A: We can express the situation as a linear equation by denoting the cost of a pen as x and the cost of a copy as y. The equation would be:

10x + 7y = 550

Q: What is the relationship between the cost of a pen and a copy?

A: The cost of one pen is Rs. 10 less than the cost of a copy. This can be expressed as:

x = y - 10

Q: How can we solve for the cost of a pen and a copy?

A: We can solve for the cost of a pen and a copy by substituting the second equation into the first equation. This will give us a linear equation in one variable, which we can then solve.

Q: What is the cost of a copy?

A: The cost of a copy is Rs. 38.24.

Q: What is the cost of a pen?

A: The cost of a pen is Rs. 28.24.

Q: What are some real-world applications of this problem?

A: Some real-world applications of this problem include:

  • Business: A company that sells pens and copies can use linear equations to determine the cost of each item and make informed business decisions.
  • Finance: A financial analyst can use linear equations to model the cost of different financial instruments and make investment decisions.
  • Science: A scientist can use linear equations to model the behavior of physical systems and make predictions about future behavior.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem include:

  • Not expressing the situation as a linear equation: Failing to express the situation as a linear equation can make it difficult to solve the problem.
  • Not using substitution: Failing to use substitution can make it difficult to solve the problem.
  • Not checking units: Failing to check units can lead to incorrect solutions.

Q: How can we use this problem to model real-world situations?

A: We can use this problem to model real-world situations by:

  • Identifying the variables: Identify the variables in the problem, such as the cost of a pen and a copy.
  • Expressing the situation as a linear equation: Express the situation as a linear equation using the variables.
  • Solving for the variables: Solve for the variables using substitution or other methods.

Q: What are some other examples of linear equations in real-world situations?

A: Some other examples of linear equations in real-world situations include:

  • Cost of goods sold: A company can use linear equations to determine the cost of goods sold and make informed business decisions.
  • Supply and demand: A company can use linear equations to model the supply and demand of a product and make predictions about future sales.
  • Financial planning: A financial analyst can use linear equations to model the cost of different financial instruments and make investment decisions.

Conclusion

In conclusion, this problem is a great example of how linear equations can be used to model real-world situations. We expressed the situation as a linear equation, solved for the cost of a pen and a copy, and discussed the real-world applications and common mistakes.