Final answer:
To find the smallest number of packs of each fruit Safoora needs to buy to have the same amount of each, calculate the Least Common Multiple (LCM) of the pack sizes (6, 5, 12), which is 60. Safoora should buy 10 packs of apples, 12 packs of bananas, and 5 packs of peaches.
Step-by-step explanation:
The question we're addressing involves finding the smallest number of packs of apples, bananas, and peaches Safoora needs to buy, such that she has the same number of each fruit. This is a common multiple problem.
- Pack of 6 apples
- Pack of 5 bananas
- Pack of 12 peaches
To solve this, we need to find the Least Common Multiple (LCM) of 6, 5, and 12, which is the smallest number that all these numbers divide into without leaving a remainder.
- Listing multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
- Listing multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
- Listing multiples of 12: 12, 24, 36, 48, 60, ...
The smallest common multiple in these lists is 60. Therefore, Safoora should buy:
- 10 packs of 6 apples (60 apples total),
- 12 packs of 5 bananas (60 bananas total), and
- 5 packs of 12 peaches (60 peaches total).
These numbers of packs will ensure she has 60 of each fruit, fulfilling the condition of having the same number of each fruit.