Math Problem Statement
Solution
This problem involves setting up a system of equations to find the weights of the large and small boxes.
Let's define:
- = weight of one large box (in pounds)
- = weight of one small box (in pounds)
From the problem, we have two key pieces of information:
- The combined weight of one large box and one small box is 85 pounds:
- The truck is carrying 60 large boxes and 70 small boxes, and the total weight is 5450 pounds:
Now we have the system of equations:
Step 1: Solve the first equation for one variable.
From , we get:
Step 2: Substitute this expression into the second equation.
Step 3: Simplify and solve for .
Step 4: Substitute into the first equation.
Final Answer:
- The weight of each large box is 50 pounds.
- The weight of each small box is 35 pounds.
Let me know if you want more details or have questions!
Here are 5 related questions:
- How would the total weight change if the truck carried 80 small boxes instead?
- What if the combined weight of a large box and a small box was different? How would that affect the equations?
- How many more large boxes can be added if the truck can carry an additional 1000 pounds?
- If the truck could carry 6000 pounds, how many more small boxes could it fit given the same weights?
- How would the solution change if we didn't know the total weight, but we knew the ratio of large to small boxes?
Tip:
When dealing with systems of equations, substitution and elimination are both powerful tools. Choose the method that simplifies the problem best!
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Equations
Linear Equations
Formulas
x + y = 85
60x + 70y = 5450
Theorems
Substitution Method for Solving Systems of Equations
Suitable Grade Level
Grades 9-11
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