Question

higher order thinking the student council was caring for the school bake sale. the members divided a type of donated item equally on plates. each plate contained only one type of item, and every plate had exactly the same number of items. there were no leftovers. what is the greatest number of items that could have been placed on each plate? bake sale donations muffins 96 breadsticks 48 rolls 84

Explanation:

Step1: Identify the problem type

We need to find the greatest number of items per plate, which means we need to find the greatest common divisor (GCD) of the number of muffins (96), breadsticks (48), and rolls (84).

Step2: Factorize each number

• Factorize 96: \( 96 = 2^5 \times 3 \)
• Factorize 48: \( 48 = 2^4 \times 3 \)
• Factorize 84: \( 84 = 2^2 \times 3 \times 7 \)

Step3: Find the common factors

The common prime factors are \( 2^2 \) and \( 3 \).

Step4: Calculate the GCD

Multiply the common prime factors with the lowest exponents: \( 2^2 \times 3 = 4 \times 3 = 12 \)

Answer:

12