Math Problem Statement

Puan Naliza baked 36 oat biscuits and 48 chocolate biscuits. She would like to divide the biscuits into packets, with each packet containing the same number of each type of biscuit. How many pieces of chocolate biscuits are in each packet?

Solution

To solve this problem, we need to divide the biscuits into packets in such a way that each packet contains the same number of oat biscuits and the same number of chocolate biscuits.

The goal is to find the largest number of biscuits that can be placed in each packet without breaking the uniformity of the distribution. This is essentially asking for the Greatest Common Divisor (GCD) of 36 (the number of oat biscuits) and 48 (the number of chocolate biscuits).

Steps to find the GCD:

  1. List the factors of 36:
    36=1,2,3,4,6,9,12,18,3636 = 1, 2, 3, 4, 6, 9, 12, 18, 36

  2. List the factors of 48:
    48=1,2,3,4,6,8,12,16,24,4848 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

  3. The common factors of 36 and 48 are:
    1,2,3,4,6,121, 2, 3, 4, 6, 12

  4. The greatest common factor (GCD) is 1212.

Thus, the biscuits can be divided into 12 packets. Each packet will contain:

  • 3612=3\frac{36}{12} = 3 oat biscuits
  • 4812=4\frac{48}{12} = 4 chocolate biscuits

Final Answer:

There are 4 chocolate biscuits in each packet.

Would you like further details on this solution or any clarifications?


Here are 5 related questions:

  1. How many oat biscuits are in each packet?
  2. How many total biscuits are there in each packet?
  3. What is the GCD of 72 and 54 biscuits?
  4. How many packets can be made if she baked 50 oat biscuits and 60 chocolate biscuits?
  5. How would the solution change if she baked 100 oat biscuits and 75 chocolate biscuits?

Tip: When dividing items into equal groups, the GCD helps find the largest possible group size that ensures equal distribution!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Greatest Common Divisor (GCD)
Division
Factors

Formulas

GCD(a, b): The greatest common divisor of a and b

Theorems

Euclidean Algorithm for GCD

Suitable Grade Level

Grades 5-7