To find the weight of the pan, we can set up a system of equations based on the information provided.
Let \( p \) be the weight of the pan, and let \( e \) be the weight of one egg. We can create the following equations:
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For the pan with four eggs: \[ p + 4e = 18 \]
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For the pan with eight eggs: \[ p + 8e = 24 \]
Now, we can solve these two equations. First, we can subtract the first equation from the second:
\[ (p + 8e) - (p + 4e) = 24 - 18 \]
This simplifies to:
\[ 4e = 6 \]
Now, divide by 4:
\[ e = \frac{6}{4} = 1.5 \text{ ounces (weight of one egg)} \]
Next, we can substitute the value of \( e \) back into one of the original equations to find \( p \). We'll use the first equation:
\[ p + 4(1.5) = 18 \]
This simplifies to:
\[ p + 6 = 18 \]
Subtract 6 from both sides:
\[ p = 18 - 6 \] \[ p = 12 \text{ ounces (weight of the pan)} \]
Therefore, the weight of the pan is 12 ounces.