How Much Did You Pay for 99 Eggs at 12 Cents a Dozen?

Imagine the scenario where you have 99 eggs, and they were priced at 12 cents per dozen. Have you ever wondered how much you would have paid for them? Let’s dive into the details and explore different methods to solve this puzzle.

The Initial Riddle

The question provides an exchange rate of 12 cents for a dozen eggs (12 eggs). However, it doesn’t specify the price for individual eggs or fractions of a dozen. This makes the problem intriguing and puzzle-like. To solve it, we need to break down the information and consider multiple scenarios.

Scenario 1: Calculating Based on Dozen Eggs

If you buy 99 eggs, you can easily determine how many dozens of eggs you need and how much it would cost:

You need 8 full dozens of eggs to have 96 eggs (8 x 12 96). This would cost you 96 cents (8 x 12 cents 96 cents). Since you have 99 eggs, you need 3 more individual eggs, which at 12 cents per dozen, would cost 3 cents. Therefore, the total cost would be 96 cents 3 cents 99 cents.

Scenario 2: Considering Fractional Dozens

Another approach is to consider the possibility of buying fractions of a dozen. Here are the steps:

Buying 8 full dozens would give you 96 eggs (8 x 12 96) and the cost of 96 cents (8 x 12 cents 96 cents). To get from 96 eggs to 99 eggs, you need 3 more individual eggs. Since a dozen eggs cost 12 cents, three individual eggs would cost 3 cents. So, the total cost would be 96 cents 3 cents 99 cents.

In this scenario, you can buy 8 full dozens and pay 96 cents, and then pay an additional 3 cents for the 3 individual eggs.

Alternative Solution: Buying Only Full Dozens

Another perspective might consider buying eggs only in full dozens, and the rest would be free:

If you buy 9 full dozens, you get 108 eggs. However, you only need 99. Therefore, you effectively buy 9 full dozens (108 eggs) and discard 9 excess eggs. The cost would be 9 full dozens:

You buy 9 full dozens of eggs (9 x 12 108 eggs). The cost for 9 full dozens is 9 x 12 cents 108 cents (or $1.08). Since you have 108 eggs and need only 99, the remaining 9 eggs are free.

Conclusion

The riddle can be solved in multiple ways, and both 99 cents and 108 cents are valid solutions depending on your interpretation of the exchange rate and the purchasing method. Understanding the details of the pricing can help in deciding the most reasonable cost.

Key Points to Remember:

12 cents for a dozen (12 eggs). 1 cent per egg. Whether eggs are sold only in full dozens or can be purchased individually.

Whether you opt for 99 cents or 108 cents, the key is to consider the exchange rate and the specific conditions given. Understanding these details will help in solving similar puzzles in the future.