Problem 16 worked answer
Pairing Packets
Designed for Grade 2 · Uses Middle Grade 2 math · About 2–6 minutes
At a glance
- Part 1: The possible totals are 14, 16, and 18 packets.
- Part 2: They make 7, 8, and 9 pairs, respectively. The other allowed totals leave one packet unpaired.
Key idea
The total must be more than 12 and fewer than 19, so the complete allowed list is 13, 14, 15, 16, 17, and 18. A total works only when groups of 2 use every packet.
1. Find every possible total
Test every allowed total:
| Packet total | Complete pairs | Result |
|---|---|---|
| 13 | 6 pairs and 1 left over | Does not work |
| 14 | 7 pairs | Works |
| 15 | 7 pairs and 1 left over | Does not work |
| 16 | 8 pairs | Works |
| 17 | 8 pairs and 1 left over | Does not work |
| 18 | 9 pairs | Works |
Therefore the complete answer is 14, 16, and 18 packets.
2. Count pairs and explain the other totals
- pairs.
- pairs.
- pairs.
The remaining allowed totals—13, 15, and 17—are odd. Pairing as many packets as possible always leaves exactly one unpaired, so the cart cannot leave with any of them.
Why the list is complete
The strict bounds exclude 12 and 19. The table checks every whole-number total between those bounds, so there is no omitted candidate.
Check
Multiplication rebuilds each working total: , , and . Every packet is used in each equation.
Technical fit and rating
Number and operations
How the rating works →mathjewels.com/answers/problems/16/