A fruit company delivers 2 types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes have a total weight of 187 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 87 kilograms. How much does each type of box weigh

Let's denote the weight of a large box as \( L \) kilograms and the weight of a small box as \( S \) kilograms.

We are given two pieces of information:

1. A delivery of 5 large boxes and 6 small boxes has a total weight of 187 kilograms:
   \[
   5L + 6S = 187
   \]

2. A delivery of 3 large boxes and 2 small boxes has a total weight of 87 kilograms:
   \[
   3L + 2S = 87
   \]

We have a system of two linear equations:
\[
\begin{align*}
5L + 6S & = 187 \quad \text{(Equation 1)} \\
3L + 2S & = 87 \quad \text{(Equation 2)}
\end{align*}
\]

### Step 1: Eliminate one variable
To eliminate one variable, let's multiply Equation 2 by 3 to match the coefficients of \( S \) in both equations:

\[
3 \times (3L + 2S) = 3 \times 87
\]

This gives us:

\[
9L + 6S = 261 \quad \text{(Equation 3)}
\]

### Step 2: Subtract Equation 1 from Equation 3
Now, subtract Equation 1 from Equation 3 to eliminate \( S \):

\[
(9L + 6S) - (5L + 6S) = 261 - 187
\]

This simplifies to:

\[
4L = 74
\]

### Step 3: Solve for \( L \)
Divide both sides by 4:

\[
L = \frac{74}{4} = 18.5
\]

### Step 4: Solve for \( S \)
Now that we have \( L = 18.5 \) kilograms, substitute this value back into Equation 2 to solve for \( S \):

\[
3(18.5) + 2S = 87
\]

\[
55.5 + 2S = 87
\]

Subtract 55.5 from both sides:

\[
2S = 31.5
\]

Divide by 2:

\[
S = \frac{31.5}{2} = 15.75
\]

### Final Answer
The weight of each type of box is:
- The large box weighs **18.5 kilograms**.
- The small box weighs **15.75 kilograms**.

Would you like further details or have any questions?

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Here are five related questions you might find interesting:

1. What is the total weight if the company delivers 7 large boxes and 5 small boxes?
2. How would the equation change if a large box weighed 20 kilograms?
3. Can you express the number of large boxes in terms of the number of small boxes for a given total weight?
4. If the weights of the boxes changed over time, how would you set up a system to account for these variations?
5. How would you approach solving this system of equations using a matrix method?

**Tip:** In problems involving multiple variables, systematically eliminate one variable at a time to simplify solving the system of equations.

Learn how to solve a system of equations involving large and small boxes with detailed step-by-step solutions. Find out the weights of large and small boxes based on given deliveries and total weights. Suitable for Grades 7-9 students learning algebra and systems of equations.

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