https://file.aiquickdraw.com/mathbot/file/17262756103824mhf34li.jpg

To solve the questions based on the image, let's break it down:

### Given:
- 312 mango bites
- 260 eclairs
- 156 coffee bites

We need to find how many toffees are in each packet such that the number of toffees in each packet is the same for all three types (mango, eclair, and coffee bites). The problem asks us to find the maximum number of toffees per packet and how many packets are required for each type.

### a) How many toffees are there in each packet?
This question is asking for the greatest common divisor (GCD) of 312, 260, and 156, as the largest possible packet will contain that many toffees.

Let me calculate the GCD for these numbers.The greatest common divisor (GCD) of 312, 260, and 156 is **52**. This means there are **52 toffees in each packet**.

### b) How many total packets are required to pack all toffees?
To find the total number of packets, divide the total number of each type of toffee by the number of toffees per packet (52).

Let's calculate that next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the total packets by following these steps:

1. **Mango bite packets:** Divide the total mango bites (312) by the number of toffees per packet (52).
   
   \( \frac{312}{52} = 6 \text{ packets} \)

2. **Eclair packets:** Divide the total eclair bites (260) by the number of toffees per packet (52).
   
   \( \frac{260}{52} = 5 \text{ packets} \)

3. **Coffee bite packets:** Divide the total coffee bites (156) by the number of toffees per packet (52).
   
   \( \frac{156}{52} = 3 \text{ packets} \)

4. **Total packets:** Add up all the packets for the different types of toffees.
   
   \( 6 + 5 + 3 = 14 \text{ total packets} \)

If you have any questions about this or want further details, feel free to ask!

Here are 5 related questions for you:
1. What would happen if we had a different number of toffees per packet?
2. Can we use the least common multiple (LCM) in some other way for similar problems?
3. What is the relationship between GCD and LCM in packing problems?
4. How would the solution change if there were an additional type of toffee?
5. How can this concept be applied to real-life packaging problems?

**Tip:** The GCD helps in optimizing resources when splitting quantities into equal parts efficiently!

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 a maximum and equal number of toffees. a) How many toffees are there in each packet? b) How many total packets are required to pack all toffees? c) How many packets are required to pack mango bite toffees? d) How many packets are required to pack eclair toffees? e) How many packets are required to pack coffee bite toffees?

Find out how to pack 312 mango bites, 260 eclairs, and 156 coffee bites into equal-sized packets using the GCD formula. This problem teaches key mathematical concepts, such as the greatest common divisor and its application in real-life scenarios. Perfect for students in Grades 6-8.

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