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:

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? --- 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.