a pan with four eggs weighs 18 ounces. A pan with eight eggs weighs 24 ounces. What is the weight of the pan?(1 point)

Question

oz.

Answer 1

Let the weight of the pan be \( p \) ounces and the weight of each egg be \( e \) ounces.

From the information given:

1. A pan with four eggs weighs 18 ounces: \[ p + 4e = 18 \]

2. A pan with eight eggs weighs 24 ounces: \[ p + 8e = 24 \]

Now, we can set up a system of equations:

1. \( p + 4e = 18 \) (Equation 1)
2. \( p + 8e = 24 \) (Equation 2)

To eliminate \( p \), we can subtract Equation 1 from Equation 2:

\[ (p + 8e) - (p + 4e) = 24 - 18 \]

This simplifies to:

\[ 4e = 6 \]

Now, solve for \( e \):

\[ e = \frac{6}{4} = \frac{3}{2} \text{ ounces} \]

Now that we know the weight of each egg, we can substitute \( e \) back into one of the original equations to find \( p \). Using Equation 1:

\[ p + 4 \left(\frac{3}{2}\right) = 18 \]

This simplifies to:

\[ p + 6 = 18 \]

Now, solve for \( p \):

\[ p = 18 - 6 = 12 \]

Thus, the weight of the pan is \( \boxed{12} \) ounces.