Carla Is Following A Recipe That Calls For A Cinnamon-sugar Mixture That Is $5\%$ Cinnamon. She Places 2 Grams Of Cinnamon In A Bowl And Correctly Uses The Equation $\frac{2}{g+2} \cdot 100=5$ To Determine How Many Grams Of Sugar To

Introduction

In this article, we will explore a mathematical problem that involves a recipe for a cinnamon-sugar mixture. The recipe calls for a mixture that is $5\%$ cinnamon, and Carla wants to determine how many grams of sugar to add to the mixture. To solve this problem, we will use a simple equation that involves the amount of cinnamon and the total weight of the mixture.

The Problem

Carla places 2 grams of cinnamon in a bowl and wants to determine how many grams of sugar to add to the mixture. The recipe calls for a mixture that is $5\%$ cinnamon, which means that the mixture should contain $5\%$ of the total weight as cinnamon. We can represent this as an equation:

$$\frac{2}{g+2} \cdot 100=5$$

where $g$ is the number of grams of sugar to add to the mixture.

Solving the Equation

To solve this equation, we can start by isolating the variable $g$. We can do this by multiplying both sides of the equation by $(g+2)$, which will eliminate the fraction:

$$\frac{2}{g+2} \cdot 100 \cdot (g+2) = 5 \cdot (g+2)$$

This simplifies to:

$$200 = 5g + 10$$

Next, we can subtract 10 from both sides of the equation to get:

$$190 = 5g$$

Finally, we can divide both sides of the equation by 5 to solve for $g$:

$$g = \frac{190}{5}$$

$$g = 38$$

Conclusion

In this article, we solved a mathematical problem that involved a recipe for a cinnamon-sugar mixture. We used a simple equation to determine how many grams of sugar to add to the mixture, given that the recipe calls for a mixture that is $5\%$ cinnamon. The solution to the equation was $g = 38$, which means that Carla should add 38 grams of sugar to the mixture.

Understanding the Solution

The solution to the equation $g = 38$ means that the mixture should contain 38 grams of sugar for every 2 grams of cinnamon. This is because the recipe calls for a mixture that is $5\%$ cinnamon, which means that the mixture should contain $5\%$ of the total weight as cinnamon. In this case, the total weight of the mixture is $2 + 38 = 40$ grams, and $5\%$ of this weight is $2$ grams of cinnamon.

Real-World Applications

The problem of determining how many grams of sugar to add to a mixture is a common problem in cooking and baking. It is often necessary to adjust the amount of sugar in a recipe to achieve the desired flavor and texture. This problem can be solved using a simple equation, as we did in this article.

Tips and Variations

• To solve this problem, we can also use a calculator to find the value of $g$.
• We can also use a graphing calculator to visualize the equation and find the value of $g$.
• We can also use a spreadsheet to solve this problem and find the value of $g$.

Conclusion

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Q: What is the problem with the cinnamon-sugar mixture equation?

A: The problem is that Carla wants to determine how many grams of sugar to add to the mixture, given that the recipe calls for a mixture that is $5\%$ cinnamon.

Q: How do we solve the equation?

A: To solve the equation, we can start by isolating the variable $g$. We can do this by multiplying both sides of the equation by $(g+2)$, which will eliminate the fraction.

Q: What is the equation that we need to solve?

A: The equation is:

$$\frac{2}{g+2} \cdot 100=5$$

Q: How do we simplify the equation?

A: We can simplify the equation by multiplying both sides of the equation by $(g+2)$, which will eliminate the fraction. This gives us:

$$200 = 5g + 10$$

Q: How do we solve for $g$?

A: We can solve for $g$ by subtracting 10 from both sides of the equation, which gives us:

$$190 = 5g$$

Then, we can divide both sides of the equation by 5 to get:

$$g = \frac{190}{5}$$

$$g = 38$$

Q: What does the solution mean?

A: The solution $g = 38$ means that Carla should add 38 grams of sugar to the mixture.

Q: Why is it important to understand the solution?

A: It is important to understand the solution because it tells us how many grams of sugar to add to the mixture to achieve the desired flavor and texture.

Q: Can we use a calculator to solve the equation?

A: Yes, we can use a calculator to solve the equation. We can simply enter the equation into the calculator and press the "solve" button to get the value of $g$.

Q: Can we use a graphing calculator to visualize the equation?

A: Yes, we can use a graphing calculator to visualize the equation. We can enter the equation into the calculator and use the "graph" function to see the relationship between $g$ and the other variables.

Q: Can we use a spreadsheet to solve the equation?

A: Yes, we can use a spreadsheet to solve the equation. We can enter the equation into the spreadsheet and use the "solve" function to get the value of $g$.

Q: What are some real-world applications of the cinnamon-sugar mixture equation?

A: Some real-world applications of the cinnamon-sugar mixture equation include:

• Baking: The equation can be used to determine the amount of sugar to add to a recipe to achieve the desired flavor and texture.
• Cooking: The equation can be used to determine the amount of sugar to add to a recipe to achieve the desired flavor and texture.
• Food science: The equation can be used to study the properties of sugar and its behavior in different mixtures.

Q: What are some tips and variations for solving the equation?

A: Some tips and variations for solving the equation include:

• Using a calculator to solve the equation.
• Using a graphing calculator to visualize the equation.
• Using a spreadsheet to solve the equation.
• Using different types of sugar, such as brown sugar or honey, to change the flavor and texture of the mixture.
• Adding other ingredients, such as spices or nuts, to change the flavor and texture of the mixture.