To solve this, we need to find the greatest number of plates Emily can prepare such that each plate has the same amount of food, with none left over. This is a problem of finding the greatest common divisor (GCD) of the number of pieces of bread (60) and the number of pieces of chicken (28).

Step 1: Find the GCD of 60 and 28

We can use the Euclidean algorithm to find the GCD of 60 and 28.

1. Divide 60 by 28, and find the remainder: $60 \div 28 = 2 \quad \text{(quotient)} \quad 60 - 28 \times 2 = 60 - 56 = 4 \quad \text{(remainder)}$

2. Now, divide 28 by the remainder 4: $28 \div 4 = 7 \quad \text{(quotient)} \quad 28 - 4 \times 7 = 28 - 28 = 0 \quad \text{(remainder)}$

Since the remainder is now 0, the GCD is the last non-zero remainder, which is 4.

Step 2: Interpretation

The greatest number of plates Emily can prepare is the GCD, which is 4. This means she can divide the 60 pieces of bread and 28 pieces of chicken into 4 plates, with each plate getting:

• $60 \div 4 = 15$ pieces of bread
• $28 \div 4 = 7$ pieces of chicken

Answer:

Emily can prepare 4 plates.

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If you'd like further explanation or more examples, feel free to ask. Here are some related questions to explore:

1. How do we calculate the GCD using prime factorization?
2. What is the difference between the greatest common divisor and the least common multiple (LCM)?
3. Can the Euclidean algorithm be used to find the GCD of more than two numbers?
4. How do we apply the GCD method to dividing items into equal groups in real-world scenarios?
5. How does the concept of GCD relate to simplifying fractions?

Tip: The Euclidean algorithm is a very efficient way to compute the GCD, especially when the numbers involved are large!