Tomas Is Making Trail Mix Using Granola And Walnuts. He Can Spend A Total Of $ $12 $ On The Ingredients. He Buys 3 Pounds Of Granola That Costs $ $2.00 $ Per Pound. The Walnuts Cost $ $6 $ Per Pound. He Uses The Equation

by ADMIN 221 views

Introduction

Tomas is on a mission to create the perfect trail mix using granola and walnuts. However, he has a limited budget of $12 to spend on the ingredients. As he navigates the world of granola and walnuts, he must use mathematical equations to determine the optimal combination of ingredients to meet his budget. In this article, we will delve into the mathematical world of Tomas' trail mix and explore the equations that govern his purchasing decisions.

The Problem

Tomas can spend a total of $12 on the ingredients. He buys 3 pounds of granola that costs $2.00 per pound. The walnuts cost $6 per pound. Tomas wants to know how many pounds of walnuts he can buy with the remaining budget. To solve this problem, we can use the equation:

Equation 1: Total Cost

Let's denote the number of pounds of walnuts as x. The total cost of the granola is 3 * $2.00 = $6.00. The total cost of the walnuts is x * $6.00. The total cost of the ingredients is the sum of the cost of the granola and the cost of the walnuts, which is equal to $12.00. Therefore, we can write the equation:

$6.00 + $6.00x = $12.00

Simplifying the Equation

To simplify the equation, we can subtract $6.00 from both sides:

$6.00x = $6.00

Dividing Both Sides

Next, we can divide both sides of the equation by $6.00:

x = 1

Conclusion

Tomas can buy 1 pound of walnuts with the remaining budget. However, this is not the only solution to the problem. We can also consider the case where Tomas buys more than 1 pound of walnuts. In this case, we can use the equation:

Equation 2: Total Cost (Multiple Pounds of Walnuts)

Let's denote the number of pounds of walnuts as x. The total cost of the granola is 3 * $2.00 = $6.00. The total cost of the walnuts is x * $6.00. The total cost of the ingredients is the sum of the cost of the granola and the cost of the walnuts, which is equal to $12.00. Therefore, we can write the equation:

$6.00 + $6.00x = $12.00

Simplifying the Equation (Multiple Pounds of Walnuts)

To simplify the equation, we can subtract $6.00 from both sides:

$6.00x = $6.00

Dividing Both Sides (Multiple Pounds of Walnuts)

Next, we can divide both sides of the equation by $6.00:

x = 1

Conclusion (Multiple Pounds of Walnuts)

Tomas can buy 1 pound of walnuts with the remaining budget. However, this is not the only solution to the problem. We can also consider the case where Tomas buys more than 1 pound of walnuts. In this case, we can use the equation:

Equation 3: Total Cost (Multiple Pounds of Granola)

Let's denote the number of pounds of granola as y. The total cost of the granola is y * $2.00. The total cost of the walnuts is x * $6.00. The total cost of the ingredients is the sum of the cost of the granola and the cost of the walnuts, which is equal to $12.00. Therefore, we can write the equation:

$2.00y + $6.00x = $12.00

Simplifying the Equation (Multiple Pounds of Granola)

To simplify the equation, we can subtract $6.00x from both sides:

$2.00y = $12.00 - $6.00x

Dividing Both Sides (Multiple Pounds of Granola)

Next, we can divide both sides of the equation by $2.00:

y = ($12.00 - $6.00x) / $2.00

Conclusion (Multiple Pounds of Granola)

Tomas can buy multiple pounds of granola and walnuts with the remaining budget. The number of pounds of granola that Tomas can buy depends on the number of pounds of walnuts that he buys.

The Final Answer

In conclusion, Tomas can buy 1 pound of walnuts with the remaining budget. However, this is not the only solution to the problem. We can also consider the case where Tomas buys more than 1 pound of walnuts or multiple pounds of granola. The number of pounds of granola that Tomas can buy depends on the number of pounds of walnuts that he buys.

Real-World Applications

The mathematical equations that govern Tomas' trail mix purchasing decisions have real-world applications in various fields, including economics, finance, and business. For example, a company may use similar equations to determine the optimal combination of ingredients for a product, given a limited budget.

Conclusion

Introduction

In our previous article, we explored the mathematical equations that govern Tomas' trail mix purchasing decisions. In this article, we will answer some of the most frequently asked questions about Tomas' trail mix conundrum.

Q: What is the total cost of the ingredients?

A: The total cost of the ingredients is $12.00.

Q: How much does the granola cost per pound?

A: The granola costs $2.00 per pound.

Q: How much does the walnuts cost per pound?

A: The walnuts cost $6.00 per pound.

Q: What is the equation that governs Tomas' purchasing decisions?

A: The equation that governs Tomas' purchasing decisions is:

$6.00 + $6.00x = $12.00

Q: What is the solution to the equation?

A: The solution to the equation is x = 1, which means that Tomas can buy 1 pound of walnuts with the remaining budget.

Q: Can Tomas buy more than 1 pound of walnuts?

A: Yes, Tomas can buy more than 1 pound of walnuts. However, the number of pounds of walnuts that Tomas can buy depends on the number of pounds of granola that he buys.

Q: What is the equation that governs the number of pounds of granola that Tomas can buy?

A: The equation that governs the number of pounds of granola that Tomas can buy is:

$2.00y = $12.00 - $6.00x

Q: How does the number of pounds of granola that Tomas can buy depend on the number of pounds of walnuts that he buys?

A: The number of pounds of granola that Tomas can buy depends on the number of pounds of walnuts that he buys. If Tomas buys more than 1 pound of walnuts, he can buy fewer pounds of granola.

Q: What are some real-world applications of the mathematical equations that govern Tomas' trail mix purchasing decisions?

A: Some real-world applications of the mathematical equations that govern Tomas' trail mix purchasing decisions include:

  • Determining the optimal combination of ingredients for a product, given a limited budget.
  • Calculating the cost of ingredients for a recipe.
  • Optimizing the production process for a company.

Q: Can Tomas' trail mix conundrum be solved using other mathematical techniques?

A: Yes, Tomas' trail mix conundrum can be solved using other mathematical techniques, such as linear programming or optimization algorithms.

Conclusion

In conclusion, Tomas' trail mix conundrum is a mathematical problem that requires the use of equations to determine the optimal combination of ingredients. The equations that govern Tomas' purchasing decisions have real-world applications in various fields, including economics, finance, and business.

Frequently Asked Questions

  • Q: What is the total cost of the ingredients?
  • A: The total cost of the ingredients is $12.00.
  • Q: How much does the granola cost per pound?
  • A: The granola costs $2.00 per pound.
  • Q: How much does the walnuts cost per pound?
  • A: The walnuts cost $6.00 per pound.
  • Q: What is the equation that governs Tomas' purchasing decisions?
  • A: The equation that governs Tomas' purchasing decisions is $6.00 + $6.00x = $12.00.
  • Q: What is the solution to the equation?
  • A: The solution to the equation is x = 1, which means that Tomas can buy 1 pound of walnuts with the remaining budget.

Glossary

  • Linear equation: An equation in which the highest power of the variable is 1.
  • Optimization algorithm: A mathematical technique used to find the optimal solution to a problem.
  • Linear programming: A mathematical technique used to find the optimal solution to a problem, given a set of linear constraints.