To determine the weights of the large and small boxes, we can set up a system of equations based on the information given.
Let:
- \( L \) = weight of a large box (in kg)
- \( S \) = weight of a small box (in kg)
From the information provided, we can formulate the following equations based on the weights of the boxes:
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For 3 large boxes and 5 small boxes: \[ 3L + 5S = 135 \quad \text{(Equation 1)} \]
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For 9 large boxes and 7 small boxes: \[ 9L + 7S = 279 \quad \text{(Equation 2)} \]
Now, we can solve this system of equations. We can start by multiplying Equation 1 by 3 to facilitate elimination:
\[ 9L + 15S = 405 \quad \text{(Equation 3)} \]
Now, we can subtract Equation 2 from Equation 3:
\[ (9L + 15S) - (9L + 7S) = 405 - 279 \]
This simplifies to:
\[ 8S = 126 \]
Now, solve for \( S \):
\[ S = \frac{126}{8} = 15.75 \]
Now that we have \( S \), we can substitute it back into Equation 1 to find \( L \):
\[ 3L + 5(15.75) = 135 \] \[ 3L + 78.75 = 135 \] \[ 3L = 135 - 78.75 \] \[ 3L = 56.25 \] \[ L = \frac{56.25}{3} = 18.75 \]
Thus, the weights of the boxes are:
- Large box (\( L \)) = 18.75 kg
- Small box (\( S \)) = 15.75 kg
Therefore, the correct answer is:
C. 18.75, 15.75
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