Math Problem Statement

There are 312 mango bites, 260 eclairs, and 156 coffee bites in a box. These are to be put in packets so that each packet contains the maximum and equal number of toffees. How many toffees are there in each packet, and how many packets are required for each type?

Solution

The problem you're working on seems to be about packing a certain number of mango bites, eclairs, and coffee bites into packets where each packet contains the maximum possible equal number of toffees. Here are the details:

  • 312 mango bites
  • 260 eclairs
  • 156 coffee bites

The questions are:

  1. How many toffees are there in each packet?

    • This requires finding the greatest common divisor (GCD) of 312, 260, and 156 to determine how many toffees each packet can hold.
  2. How many total packets are required to pack all toffees?

    • Once the number of toffees in each packet is known, divide the total number of each type of toffee by that number to find the number of packets for each type.
  3. How many packets are required to pack mango bites?

    • Divide the total mango bites by the number of toffees in each packet.
  4. How many packets are required to pack eclairs?

    • Similarly, divide the total eclairs by the number of toffees in each packet.
  5. How many packets are required to pack coffee bites?

    • Do the same for coffee bites.

Let me compute the GCD and determine the answers to these questions.Here are the results:

  1. Number of toffees in each packet: 52
  2. Total packets required to pack all toffees: 14 packets
  3. Packets required to pack mango bites: 6 packets
  4. Packets required to pack eclairs: 5 packets
  5. Packets required to pack coffee bites: 3 packets

Let me know if you need further details!

Here are some related questions for better understanding:

  1. What if the number of mango bites increased to 350? How would that change the number of packets?
  2. How do we find the greatest common divisor (GCD) of three numbers?
  3. What would happen if the GCD of these numbers was 1?
  4. How can we calculate the least common multiple (LCM) instead of the GCD?
  5. If the toffees per packet were different for each type, how would you organize the packing?

Tip: GCD is useful for dividing items into equal groups, but the Least Common Multiple (LCM) is helpful when looking to synchronize intervals or tasks.

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Math Problem Analysis

Mathematical Concepts

Greatest Common Divisor (GCD)
Division

Formulas

GCD(a, b, c) = GCD(GCD(a, b), c)
Number of packets = Total number of items / GCD

Theorems

Euclidean algorithm for finding GCD

Suitable Grade Level

Grades 6-8