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.