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A pan with 2 eggs weighs 9 ounces. A pan with four eggs weighs 12 ounces. What is the weight of the pan?

A. 6 oz.
B. 12 oz.
C. 9 oz.
D. 3 oz.

Answer :

To solve the problem of finding the weight of the pan, let's explore the information provided:

  1. A pan with 2 eggs weighs 9 ounces.
  2. A pan with 4 eggs weighs 12 ounces.

Let's denote:

  • [tex]P[/tex] as the weight of the pan.
  • [tex]E[/tex] as the weight of one egg.

From the first situation:
[tex]P + 2E = 9[/tex]

From the second situation:
[tex]P + 4E = 12[/tex]

Now, we have a system of two linear equations:

  1. [tex]P + 2E = 9[/tex]
  2. [tex]P + 4E = 12[/tex]

To find the values of [tex]P[/tex] and [tex]E[/tex], we can use the subtraction method. Subtract the first equation from the second:
[tex](P + 4E) - (P + 2E) = 12 - 9[/tex]
[tex]P + 4E - P - 2E = 3[/tex]
[tex]2E = 3[/tex]
[tex]E = \frac{3}{2}[/tex]

Now that we have [tex]E = \frac{3}{2}[/tex] ounces, substitute this back into the first equation:
[tex]P + 2 \left( \frac{3}{2} \right) = 9[/tex]
[tex]P + 3 = 9[/tex]
[tex]P = 9 - 3[/tex]
[tex]P = 6[/tex]

Therefore, the weight of the pan is [tex]\boxed{6}[/tex] ounces.

The correct choice is A. 6 oz.

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Rewritten by : Barada