Nurul is packing muffins for a school bake sale. She can fill trays of 7 or 11 muffins with no muffins left over. If she uses boxes that hold 13 muffins, 12 muffins are left over. What is the smallest possible number of trays of 7 muffins that Nurul can fill?
- Find the smallest possible total number of muffins that can be packed with no muffins left over in trays of 7 or 11.
- Check the condition for boxes of 13, then find the number of trays of 7 muffins that Nurul can fill.
Need a hint?
Find the smallest number of muffins that both tray sizes divide exactly. Then check what is left over when you share it into boxes of 13.
Worked answer
- (a) The total must be a multiple of both 7 and 11. The smallest common multiple is 7 × 11 = 77.
- (b) Check the boxes of 13: 77 ÷ 13 = 5 remainder 12. ✓
- The number of trays of 7 is 77 ÷ 7 = 11.
Answer: 11 trays
The mistake this question tests
Habit
Factors and multiples (HCF, LCM)
Adding 7 and 11 gives 18, but the total must be divisible by both tray sizes. Use the smallest common multiple and then divide by 7.
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