A moving company weighs 20 boxes you have packed that contain either books or clothes and says the total weight is 404 pounds. You know that a box of books weighs 40 pounds and a box of clothes weighs
7 pounds. Write and solve an equation to find how many boxes of books and how many boxes of clothes you packed.

Let's define the problem with variables:

- Let \( x \) be the number of boxes of books.
- Let \( y \) be the number of boxes of clothes.

Given:
- The total number of boxes is 20, so:
  \[
  x + y = 20
  \]
- The total weight of the boxes is 404 pounds. Since each box of books weighs 40 pounds and each box of clothes weighs 7 pounds, the total weight equation is:
  \[
  40x + 7y = 404
  \]

Now, we have a system of two equations:
\[
\begin{aligned}
1. & \quad x + y = 20 \\
2. & \quad 40x + 7y = 404
\end{aligned}
\]

### Step 1: Solve the first equation for \( y \)
\[
y = 20 - x
\]

### Step 2: Substitute \( y = 20 - x \) into the second equation
\[
40x + 7(20 - x) = 404
\]

### Step 3: Simplify and solve for \( x \)
\[
40x + 140 - 7x = 404
\]
\[
33x + 140 = 404
\]
\[
33x = 404 - 140
\]
\[
33x = 264
\]
\[
x = \frac{264}{33}
\]
\[
x = 8
\]

So, there are 8 boxes of books.

### Step 4: Use \( x = 8 \) to find \( y \)
\[
y = 20 - 8 = 12
\]

So, there are 12 boxes of clothes.

### Final Answer
- Number of boxes of books: \( 8 \)
- Number of boxes of clothes: \( 12 \)

Would you like more details on any step, or do you have any questions? Here are some related questions you might find helpful:

1. How can you check your solution for a system of equations?
2. What if a box of books weighed 50 pounds instead? How would that change the solution?
3. How can you graphically represent the system of equations?
4. What method would you use if the coefficients were not integers?
5. Can you use matrices to solve this system of equations?

**Tip:** When solving systems of equations, substitution is often easier when one equation is already solved for a variable, as in this case.

Learn how to solve a system of equations involving boxes of books and clothes. Understand the method of substitution to find the number of boxes of each type based on their weights and total number.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation