Problem 9 answer key

Nurse Joy’s Poké Ball Packs

Grade 2 · Number and operations

MJ 2.7 · C3 · W2 Stretch challenge · Moderate workload

About 6–15 minutes

4 jewels

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 = 14 containers.

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:

  1. Trade one 100-ball crate for 10 small boxes: (1, 14, 8).
  2. 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.

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