https://file.aiquickdraw.com/mathbot/file/1730144210687ktbgwcqt.jpg

Let's set up equations based on the information given.

1. **Define Variables:**
   - Let $ b $ be the cost of 1 loaf of bread.
   - Let $ e $ be the cost of 1 dozen eggs.

2. **Translate the Information into Equations:**
   - The first customer’s purchase:
     \[
     b + 2e = 12.45
     \]
   - The second customer’s purchase:
     \[
     4b + e = 19.42
     \]

3. **Solve the System of Equations:**
   - From the second equation, we can isolate $ e $:
     \[
     e = 19.42 - 4b
     \]
   - Substitute $ e $ from the second equation into the first equation:
     \[
     b + 2(19.42 - 4b) = 12.45
     \]
   - Simplify and solve for $ b $:
     \[
     b + 38.84 - 8b = 12.45
     \]
     \[
     -7b = 12.45 - 38.84
     \]
     \[
     -7b = -26.39
     \]
     \[
     b = 3.77
     \]

4. **Find $ e $:**
   - Substitute $ b = 3.77 $ into $ e = 19.42 - 4b $:
     \[
     e = 19.42 - 4(3.77)
     \]
     \[
     e = 19.42 - 15.08
     \]
     \[
     e = 4.34
     \]

So, the cost of 1 dozen eggs is **$4.34**.

### Answer:
The correct answer is $ \text{D) } 4.34 $.

Would you like further details on this solution, or do you have any questions?

### Related Questions:
1. What would the cost be for 3 loaves of bread and 2 dozen eggs?
2. If the price of eggs increases by 10%, what would the new price be for 1 dozen eggs?
3. How would the total cost change if each loaf of bread was $0.50 more expensive?
4. Can this method be used to find the price of items with more than two variables?
5. How do we verify if both equations are consistent for a unique solution?

### Tip:
When solving for two variables, look for ways to isolate one variable and substitute it into the other equation. This method, substitution, often simplifies the process.

Two customers purchased the same kind of bread and eggs at a store. The first customer paid 12.45 dollars for 1 loaf of bread and 2 dozen eggs. The second customer paid 19.42 dollars for 4 loaves of bread and 1 dozen eggs. What is the cost, in dollars, of 1 dozen eggs?

Learn how to solve for the cost of 1 dozen eggs when given the prices for different combinations of bread and eggs. This algebra problem involves setting up and solving a system of linear equations, using substitution. Ideal for students in Grades 8-10.

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