The problem involves a delivery truck transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is given as 65 pounds, and the truck is transporting 50 large boxes and 65 small boxes, with a total weight of 3,550 pounds. We need to determine the weight of each type of box.

Let:

• $x$ = weight of a large box in pounds
• $y$ = weight of a small box in pounds

We know the following:

1. The combined weight of a large and small box is 65 pounds:
   $x + y = 65$
2. The total weight of all the boxes (50 large and 65 small) is 3,550 pounds:
   $50x + 65y = 3550$

We now solve this system of equations.

Step 1: Solve for one variable

From the first equation, we can express $x$ in terms of $y$: $x = 65 - y$

Step 2: Substitute into the second equation

Substitute $x = 65 - y$ into the second equation: $50(65 - y) + 65y = 3550$ $3250 - 50y + 65y = 3550$ $3250 + 15y = 3550$ $15y = 3550 - 3250$ $15y = 300$ $y = \frac{300}{15} = 20$

Step 3: Find $x$

Substitute $y = 20$ into $x = 65 - y$: $x = 65 - 20 = 45$

Conclusion

• The large box weighs 45 pounds.
• The small box weighs 20 pounds.

Would you like further explanation or details on any part of the solution? Here are five related questions:

1. How can systems of equations be solved graphically?
2. What other methods could be used to solve systems of equations besides substitution?
3. How can word problems like this be represented as systems of equations?
4. What would happen if the weight of the boxes was given differently?
5. How do you know the solution to a system of equations is correct?

Tip: Always check your solution by substituting the values back into both original equations to ensure they satisfy both conditions!