Problem 9 answer key
Nurse Joy’s Poké Ball Packs
Grade 2 · Number and operations
About 6–15 minutes
Nurse Joy’s Poké Ball Packs — answer
Problem ID: 9
Start with the usual place-value packing:
248 = 2 hundreds + 4 tens + 8 ones- That would use
2 + 4 + 8 = 14containers.
Nurse Joy needs 23 containers, which is 9 more. Trading one full container for 10 of the next smaller kind keeps the number of Poké Balls the same and adds exactly 9 containers.
There are two possible one-trade packings:
- Trade one 100-ball crate for 10 small boxes:
(1, 14, 8). - Trade one 10-ball box for 10 one-ball sleeves:
(2, 3, 18).
The second packing has z = 18 one-ball sleeves but only 3 small boxes, so it does not have more small boxes than sleeves.
Check the remaining packing:
- Poké Balls:
1 × 100 + 14 × 10 + 8 × 1 = 248 - Containers:
1 + 14 + 8 = 23 - Comparison:
14 > 8
Answer: 1 large crate, 14 small boxes, and 8 one-ball sleeves.
This answer is unique because 248 can use only 1 or 2 large crates when exactly 23 full containers are used. Those two cases give the two packings above, and only (1, 14, 8) satisfies the final comparison.