Question

a pan with 4 eggs weighs 18 ounces and a pan with 8 eggs weighs 24 ounces, how much does the pan weigh

Answer 1

Let's denote the weight of the pan as \( P \) ounces and the weight of each egg as \( E \) ounces.

From the information provided, we can set up two equations based on the weights given:

1. For the pan with 4 eggs:
\[
P + 4E = 18
\]

2. For the pan with 8 eggs:
\[
P + 8E = 24
\]

Now, we can solve these two equations. First, we can isolate \( P \) in both equations:

From the first equation:
\[
P = 18 - 4E
\]

From the second equation:
\[
P = 24 - 8E
\]

Now we can set these two expressions for \( P \) equal to each other:
\[
18 - 4E = 24 - 8E
\]

To solve for \( E \), we can rearrange and simplify this equation:
\[
8E - 4E = 24 - 18
\]
\[
4E = 6
\]
\[
E = \frac{6}{4} = 1.5 \text{ ounces (weight of each egg)}
\]

Now, we can substitute \( E \) back into one of the original equations to find \( P \). Using the first equation:
\[
P + 4(1.5) = 18
\]
\[
P + 6 = 18
\]
\[
P = 18 - 6
\]
\[
P = 12 \text{ ounces (weight of the pan)}
\]

So, the weight of the pan is **12 ounces**.