Bob Has Some 10 Lb Weights And Some 3 Lb Weights. Together, All His Weights Add Up To 50 Lb. If $x$ Represents The Number Of 3 Lb Weights And $y$ Represents The Number Of 10 Lb Weights, Which Equation Can Be Used To Find The Number Of

Introduction

In this article, we will delve into a mathematical problem that involves solving an equation to find the number of 3 lb weights and 10 lb weights that Bob has. The problem states that Bob has some 10 lb weights and some 3 lb weights, and together, all his weights add up to 50 lb. We will use algebraic equations to represent the problem and solve for the unknown variables.

Understanding the Problem

Let's break down the problem and understand what is being asked. We have two types of weights: 3 lb weights and 10 lb weights. We are asked to find the number of each type of weight that Bob has. Let's represent the number of 3 lb weights as $x$ and the number of 10 lb weights as $y$.

Setting Up the Equation

Since the total weight of all the weights is 50 lb, we can set up an equation to represent this situation. The total weight is the sum of the weights of the 3 lb weights and the 10 lb weights. We can write this as:

3x + 10y = 50

This equation states that the total weight is equal to the sum of the weights of the 3 lb weights and the 10 lb weights.

Solving the Equation

To solve for $x$ and $y$, we need to isolate one of the variables. Let's isolate $x$ by subtracting 10y from both sides of the equation:

3x = 50 - 10y

Now, we can divide both sides of the equation by 3 to solve for $x$:

x = (50 - 10y) / 3

This equation represents the number of 3 lb weights in terms of the number of 10 lb weights.

Finding the Number of 3 lb Weights

To find the number of 3 lb weights, we need to know the value of $y$, which represents the number of 10 lb weights. Let's assume that Bob has 2 10 lb weights, so $y = 2$. We can substitute this value into the equation for $x$:

x = (50 - 10(2)) / 3

x = (50 - 20) / 3

x = 30 / 3

x = 10

So, if Bob has 2 10 lb weights, he has 10 3 lb weights.

Finding the Number of 10 lb Weights

To find the number of 10 lb weights, we need to know the value of $x$, which represents the number of 3 lb weights. Let's assume that Bob has 5 3 lb weights, so $x = 5$. We can substitute this value into the equation for $y$:

3(5) + 10y = 50

15 + 10y = 50

Subtracting 15 from both sides of the equation:

10y = 35

Dividing both sides of the equation by 10:

y = 35 / 10

y = 3.5

So, if Bob has 5 3 lb weights, he has 3.5 10 lb weights.

Conclusion

In this article, we solved a mathematical problem that involved finding the number of 3 lb weights and 10 lb weights that Bob has. We set up an equation to represent the problem and solved for the unknown variables. We found that if Bob has 2 10 lb weights, he has 10 3 lb weights, and if Bob has 5 3 lb weights, he has 3.5 10 lb weights.

References

• Algebraic Equations
• Linear Equations

Further Reading

• Mathematics
• Algebra

Glossary

• Algebraic Equation: An equation that involves variables and constants.
• Linear Equation: An equation that can be written in the form ax + by = c, where a, b, and c are constants.
• Variable: A value that can change in a mathematical expression.
• Constant: A value that does not change in a mathematical expression.
  Frequently Asked Questions: Solving the Weighty Problem ===========================================================

Q: What is the equation that represents the problem?

A: The equation that represents the problem is 3x + 10y = 50, where x represents the number of 3 lb weights and y represents the number of 10 lb weights.

Q: How do I solve for x and y?

A: To solve for x and y, you need to isolate one of the variables. Let's isolate x by subtracting 10y from both sides of the equation:

3x = 50 - 10y

Now, you can divide both sides of the equation by 3 to solve for x:

x = (50 - 10y) / 3

Q: How do I find the number of 3 lb weights?

A: To find the number of 3 lb weights, you need to know the value of y, which represents the number of 10 lb weights. Let's assume that Bob has 2 10 lb weights, so y = 2. We can substitute this value into the equation for x:

x = (50 - 10(2)) / 3

x = (50 - 20) / 3

x = 30 / 3

x = 10

So, if Bob has 2 10 lb weights, he has 10 3 lb weights.

Q: How do I find the number of 10 lb weights?

A: To find the number of 10 lb weights, you need to know the value of x, which represents the number of 3 lb weights. Let's assume that Bob has 5 3 lb weights, so x = 5. We can substitute this value into the equation for y:

3(5) + 10y = 50

15 + 10y = 50

Subtracting 15 from both sides of the equation:

10y = 35

Dividing both sides of the equation by 10:

y = 35 / 10

y = 3.5

So, if Bob has 5 3 lb weights, he has 3.5 10 lb weights.

Q: What if I have more than one 10 lb weight?

A: If you have more than one 10 lb weight, you can substitute the value of y into the equation for x. For example, if you have 3 10 lb weights, so y = 3, we can substitute this value into the equation for x:

x = (50 - 10(3)) / 3

x = (50 - 30) / 3

x = 20 / 3

x = 6.67

So, if Bob has 3 10 lb weights, he has 6.67 3 lb weights.

Q: What if I have more than one 3 lb weight?

A: If you have more than one 3 lb weight, you can substitute the value of x into the equation for y. For example, if you have 4 3 lb weights, so x = 4, we can substitute this value into the equation for y:

3(4) + 10y = 50

12 + 10y = 50

Subtracting 12 from both sides of the equation:

10y = 38

Dividing both sides of the equation by 10:

y = 38 / 10

y = 3.8

So, if Bob has 4 3 lb weights, he has 3.8 10 lb weights.

Q: Can I use this equation to solve other problems?

A: Yes, you can use this equation to solve other problems that involve finding the number of weights. Just substitute the values of x and y into the equation and solve for the unknown variable.

Q: What if I have different weights?

A: If you have different weights, you can use a similar equation to solve the problem. For example, if you have 5 lb weights and 10 lb weights, you can set up an equation like this:

5x + 10y = 50

Where x represents the number of 5 lb weights and y represents the number of 10 lb weights.

Conclusion

In this article, we answered some frequently asked questions about solving the weighty problem. We covered topics such as solving for x and y, finding the number of 3 lb weights, and finding the number of 10 lb weights. We also discussed how to use the equation to solve other problems and how to adapt it to different weights.