To ensure that Thandi has an equal number of packets of sugar, packets of flour, and bags of rice for each combo, we need to find the least common multiple (LCM) of the quantities per carton:

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

The LCM of 20, 12, and 15 will give the minimum number of each item needed for equal combos.

Step-by-Step Solution

1. Prime Factorizations:

   • 20 = $2^2 \times 5$
   • 12 = $2^2 \times 3$
   • 15 = $3 \times 5$

2. Take the Highest Power of Each Prime:

   • For $2$: $2^2 = 4$
   • For $3$: $3^1 = 3$
   • For $5$: $5^1 = 5$

3. Calculate the LCM: $\text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$

So, the LCM is 60. This means Thandi should have 60 packets of each item (sugar, flour, and rice) to have equal quantities for each combo.

Cartons Needed for Each Item

To get 60 packets/bags for each:

• Sugar: $\frac{60}{20} = 3$ cartons
• Flour: $\frac{60}{12} = 5$ cartons
• Rice: $\frac{60}{15} = 4$ cartons

Conclusion

Thandi should buy:

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

This will give her an equal number (60) of each item for her grocery combos.

Would you like further details on the solution or have any questions?

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Related Questions:

1. What if Thandi wants to make combos with half the quantity—how many cartons would she need?
2. How would the answer change if sugar packets came in 10 per carton?
3. How would Thandi calculate the cost if each carton has a different price?
4. How could Thandi handle a situation where items are sold individually rather than in cartons?
5. What if Thandi wants to add a fourth item to the combo?

Tip: For problems involving equal quantities across multiple groups, finding the LCM helps ensure balanced sets.