A Customer At A Store Paid \$64 For 3 Large Candles And 4 Small Candles. At The Same Store, A Second Customer Paid \$4 More Than The First Customer For 1 Large Candle And 8 Small Candles. The Price Of Each Large Candle Is The Same, And The

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Introduction

Mathematics is a fascinating subject that surrounds us in our daily lives. From the prices we pay for goods and services to the distances we travel, mathematics plays a crucial role in understanding the world around us. In this article, we will delve into a real-life scenario involving candles and explore the mathematical concepts that underlie the prices paid by two customers at a store.

The Problem

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is also the same. We need to determine the price of each large candle and the price of each small candle.

Let's Break Down the Problem

Let's denote the price of each large candle as L and the price of each small candle as S. We can set up two equations based on the information provided:

  • The first customer paid $64 for 3 large candles and 4 small candles, so we can write the equation: 3L + 4S = 64
  • The second customer paid $4 more than the first customer for 1 large candle and 8 small candles, so we can write the equation: L + 8S = 64 + 4 = 68

Solving the Equations

We can solve these equations using the method of substitution or elimination. Let's use the elimination method to eliminate one of the variables.

First, we can multiply the second equation by 3 to get:

3L + 24S = 204

Now, we can subtract the first equation from this new equation to eliminate the variable L:

(3L + 24S) - (3L + 4S) = 204 - 64 20S = 140

Finding the Price of Each Small Candle

Now that we have the value of 20S, we can divide both sides by 20 to find the price of each small candle:

S = 140/20 S = 7

Finding the Price of Each Large Candle

Now that we have the price of each small candle, we can substitute this value into one of the original equations to find the price of each large candle. Let's use the first equation:

3L + 4S = 64 3L + 4(7) = 64 3L + 28 = 64

Solving for L

Now, we can subtract 28 from both sides to isolate the term with L:

3L = 64 - 28 3L = 36

Finding the Price of Each Large Candle

Finally, we can divide both sides by 3 to find the price of each large candle:

L = 36/3 L = 12

Conclusion

In this article, we used mathematical concepts to solve a real-life problem involving candles. We set up two equations based on the prices paid by two customers and used the elimination method to solve for the price of each large candle and the price of each small candle. The price of each large candle is $12, and the price of each small candle is $7.

Real-World Applications

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

  • Retail: Understanding the prices of goods and services is crucial for retailers to make informed decisions about pricing and inventory management.
  • Economics: The concept of supply and demand plays a significant role in determining prices, and understanding this concept is essential for economists to analyze market trends and make predictions.
  • Business: Companies use mathematical models to optimize their pricing strategies and make informed decisions about investments and resource allocation.

Final Thoughts

Mathematics is a powerful tool that can be used to solve complex problems and make informed decisions. By applying mathematical concepts to real-life scenarios, we can gain a deeper understanding of the world around us and make more informed decisions. Whether it's pricing candles or analyzing market trends, mathematics plays a crucial role in understanding the world around us.

References

Additional Resources

Q&A: A Customer at a Store Paid $64 for 3 Large Candles and 4 Small Candles

Q: What is the price of each large candle and the price of each small candle?

A: The price of each large candle is $12, and the price of each small candle is $7.

Q: How did you determine the price of each large candle and the price of each small candle?

A: We set up two equations based on the prices paid by two customers and used the elimination method to solve for the price of each large candle and the price of each small candle.

Q: What are the two equations that we used to solve for the price of each large candle and the price of each small candle?

A: The two equations are:

  • 3L + 4S = 64
  • L + 8S = 68

Q: How did you solve the two equations?

A: We used the elimination method to eliminate one of the variables. We multiplied the second equation by 3 to get:

3L + 24S = 204

Then, we subtracted the first equation from this new equation to eliminate the variable L:

(3L + 24S) - (3L + 4S) = 204 - 64 20S = 140

Q: How did you find the price of each small candle?

A: We divided both sides by 20 to find the price of each small candle:

S = 140/20 S = 7

Q: How did you find the price of each large candle?

A: We substituted the value of S into one of the original equations to find the price of each large candle. We used the first equation:

3L + 4S = 64 3L + 4(7) = 64 3L + 28 = 64

Then, we subtracted 28 from both sides to isolate the term with L:

3L = 64 - 28 3L = 36

Finally, we divided both sides by 3 to find the price of each large candle:

L = 36/3 L = 12

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

A: This problem has real-world applications in various fields, such as:

  • Retail: Understanding the prices of goods and services is crucial for retailers to make informed decisions about pricing and inventory management.
  • Economics: The concept of supply and demand plays a significant role in determining prices, and understanding this concept is essential for economists to analyze market trends and make predictions.
  • Business: Companies use mathematical models to optimize their pricing strategies and make informed decisions about investments and resource allocation.

Q: What is the importance of mathematics in understanding the world around us?

A: Mathematics is a powerful tool that can be used to solve complex problems and make informed decisions. By applying mathematical concepts to real-life scenarios, we can gain a deeper understanding of the world around us and make more informed decisions.

Q: What are some additional resources for learning more about systems of equations and linear algebra?

A: Some additional resources for learning more about systems of equations and linear algebra include:

Q: What are some common mistakes to avoid when solving systems of equations?

A: Some common mistakes to avoid when solving systems of equations include:

  • Not checking for extraneous solutions: Make sure to check for extraneous solutions when solving systems of equations.
  • Not using the correct method: Make sure to use the correct method for solving systems of equations, such as the elimination method or the substitution method.
  • Not checking for consistency: Make sure to check for consistency when solving systems of equations.

Q: What are some tips for solving systems of equations?

A: Some tips for solving systems of equations include:

  • Use the elimination method: The elimination method is a powerful tool for solving systems of equations.
  • Use the substitution method: The substitution method is another powerful tool for solving systems of equations.
  • Check for extraneous solutions: Make sure to check for extraneous solutions when solving systems of equations.
  • Check for consistency: Make sure to check for consistency when solving systems of equations.