A logistics company packages cargo using three types of containers: small, medium, and large.
- A shipment of small, medium, and large container has a total weight of kilograms.
- A shipment of small, medium, and large containers has a total weight of kilograms.
- A shipment of small, medium, and large containers has a total weight of kilograms.
What is the weight, in kilograms, of one large container?
Answer: 35 kilograms
Answer
The weight of one large container is 35 kilograms.
Representing the weights of small, medium, and large containers as variables , , and yields the 3x3 system of linear equations:
1)
2)
3)
Solving for in equation (2) gives . Substituting this into equations (1) and (3) reduces the system to:
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Subtracting the first equation from the second yields , so . Substituting into gives , which simplifies to .
1)
2)
3)
Solving for in equation (2) gives . Substituting this into equations (1) and (3) reduces the system to:
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Subtracting the first equation from the second yields , so . Substituting into gives , which simplifies to .
Step-by-Step Solution
Key Concept
Solving 3x3 Systems of Linear Equations using Substitution and Elimination