Molly Shared A Spool Of Ribbon With 12 People. Each Person Received 3 Feet Of Ribbon. Which Equation Can She Use To Find $r$, The Number Of Feet Of Ribbon That Her Spool Originally Had?A. $3 + R = 12$B. $r - 3 = 12$C. $3r

Introduction

In this article, we will explore a simple yet interesting problem involving a spool of ribbon shared among 12 people. Each person received 3 feet of ribbon, and we need to find the original length of the ribbon on the spool. We will use algebraic equations to solve this problem and determine the correct equation to find the number of feet of ribbon that the spool originally had.

Understanding the Problem

Molly shared a spool of ribbon with 12 people. Each person received 3 feet of ribbon. To find the original length of the ribbon on the spool, we need to use an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

The Correct Equation

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

The Correct Equation: A Simple Algebraic Manipulation

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

Let's denote the original length of the ribbon as $r$. Since each person received 3 feet of ribbon, the total length of ribbon given out is $12 \times 3 = 36$ feet. This means that the original length of the ribbon, $r$, minus the length of ribbon given out, 36 feet, is equal to 0, since the ribbon was shared equally among the 12 people.

Mathematically, this can be represented as:

$$r - 36 = 0$$

However, we can simplify this equation by adding 36 to both sides, which gives us:

$$r = 36$$

But this is not the correct equation to find the original length of the ribbon. We need to find an equation that relates the number of people, the length of ribbon each person received, and the original length of the ribbon.

$$$$$$

Q&A: Solving the Ribbon Problem

Q: What is the problem about? A: The problem is about a spool of ribbon that Molly shared with 12 people. Each person received 3 feet of ribbon, and we need to find the original length of the ribbon on the spool.

Q: What is the correct equation to find the original length of the ribbon? A: The correct equation is $r = 12 \times 3 + r$, where $r$ is the original length of the ribbon.

Q: Why is this equation correct? A: This equation is correct because it takes into account the number of people (12) and the length of ribbon each person received (3 feet). The equation states that the original length of the ribbon, $r$, is equal to the total length of ribbon given out (12 people x 3 feet/person) plus the original length of the ribbon, $r$.

Q: How do we simplify this equation? A: We can simplify this equation by subtracting $r$ from both sides, which gives us:

$$12 \times 3 = r$$

Q: What is the value of $r$? A: The value of $r$ is 36 feet.

Q: Why is this equation not correct? A: This equation is not correct because it does not take into account the fact that the ribbon was shared equally among the 12 people. The correct equation should be:

$$r - 12 \times 3 = 0$$

Q: How do we solve this equation? A: We can solve this equation by adding $12 \times 3$ to both sides, which gives us:

$$r = 12 \times 3$$

Q: What is the value of $r$? A: The value of $r$ is 36 feet.

Q: What is the difference between the correct and incorrect equations? A: The correct equation takes into account the fact that the ribbon was shared equally among the 12 people, while the incorrect equation does not.

Q: Why is it important to use the correct equation? A: It is important to use the correct equation because it will give us the correct value of $r$, which is the original length of the ribbon.

Q: Can we use the equation $r - 3 = 12$ to find the original length of the ribbon? A: No, we cannot use this equation to find the original length of the ribbon. This equation is incorrect because it does not take into account the fact that the ribbon was shared equally among the 12 people.

Q: Can we use the equation $3r = 12$ to find the original length of the ribbon? A: No, we cannot use this equation to find the original length of the ribbon. This equation is incorrect because it does not take into account the fact that the ribbon was shared equally among the 12 people.

Conclusion

In conclusion, the correct equation to find the original length of the ribbon is $r = 12 \times 3 + r$. We can simplify this equation by subtracting $r$ from both sides, which gives us:

$$12 \times 3 = r$$

The value of $r$ is 36 feet. It is important to use the correct equation to find the original length of the ribbon, as it will give us the correct value of $r$.