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We can solve this system of equations by assigning variables to each fruit's weight:

Let:
- \( x \) = weight of an orange,
- \( y \) = weight of an apple,
- \( z \) = weight of a banana.

From the given information, we can write three equations:

1. \( 3x + 2y + z = 15 \) (from the first box),
2. \( 5x + 7y + 2z = 44 \) (from the second box),
3. \( x + 3y + 5z = 26 \) (from the third box).

Now, we will solve this system of equations to find the weights of each fruit. Let's proceed with solving it.The solution to the system of equations is:

- The weight of an orange (\(x\)) is 1 unit,
- The weight of an apple (\(y\)) is 5 units,
- The weight of a banana (\(z\)) is 2 units.

Would you like further details or have any questions about the solution?

Here are 5 related questions to expand on this topic:
1. How can systems of equations be solved using substitution or elimination methods?
2. What other real-world problems can be modeled using systems of equations?
3. How does matrix algebra help in solving larger systems of equations?
4. What are some common methods for checking the consistency of a system of equations?
5. Can this system of equations be solved graphically, and how would that process work?

**Tip:** When solving a system of linear equations, always ensure that the number of independent equations matches the number of variables to guarantee a unique solution.

A box containing 3 oranges, 2 apples, and one banana weighs 15 units. Another box containing 5 oranges, 7 apples, and 2 bananas weighs 44 units. A third box containing 1 orange, 3 apples, and 5 bananas weighs 26 units. How much does each fruit weigh?

Learn how to solve a system of linear equations to determine the weights of oranges, apples, and bananas from given conditions. This problem involves three equations and covers key algebraic concepts like solving systems of equations. Suitable for high school students in Grades 9-12.

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