To ensure Thandi has an equal number of packets of sugar, packets of flour, and bags of rice in each combo, we need to find the smallest number that is a multiple of the quantities in each carton for all items.

• Sugar packets per carton = 20
• Flour packets per carton = 12
• Rice bags per carton = 15

Solution

1. Find the Least Common Multiple (LCM) of 20, 12, and 15. This will give us the smallest number of packets/bags for each product type that will allow the quantities to match.

2. The LCM of 20, 12, and 15 is 60.

   • $20 \times 3 = 60$
   • $12 \times 5 = 60$
   • $15 \times 4 = 60$

3. Calculate the number of cartons for each item:

   • For sugar, she needs $3$ cartons (since $20 \times 3 = 60$).
   • For flour, she needs $5$ cartons (since $12 \times 5 = 60$).
   • For rice, she needs $4$ cartons (since $15 \times 4 = 60$).

Answer

Thandi should buy:

• 3 cartons of sugar,
• 5 cartons of flour,
• 4 cartons of rice.

This will give her 60 packets of sugar, 60 packets of flour, and 60 bags of rice, allowing her to create equal combos.

Would you like more details on this solution, or do you have any other questions?

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1. What is the LCM and why is it useful in this context?
2. How can Thandi adjust her order if she wants to create more than 60-packet combos?
3. What if Thandi added a new item with a different carton size; how would that affect her calculation?
4. Could she reduce costs by finding a way to have fewer items while maintaining equal numbers in each combo?
5. How would the approach change if the items came in non-uniform carton sizes (like random numbers of packets)?

Tip: The LCM helps find the smallest shared multiple, making it ideal for equalizing quantities in scenarios like this.