Problem 9 worked answer
Nurse Joy’s Poké Ball Packs
Designed for Grade 2 · Uses Late Grade 2 math · About 6–15 minutes
At a glance
- Part 1: Nurse Joy uses 1 large crate, 14 small boxes, and 8 one-ball sleeves.
Key idea
The usual place-value packing of 248 is 2 hundreds, 4 tens, and 8 ones. That uses only containers. Nurse Joy needs 23 containers, which is 9 more.
Trading one full container for 10 containers of the next smaller size keeps the number of Poké Balls unchanged and increases the container count by 9.
1. Find the packing
There are two ways to make one such trade from the usual packing:
- Trade one 100-ball crate for 10 small boxes. This gives : 1 large crate, 14 small boxes, and 8 sleeves.
- Trade one 10-ball box for 10 one-ball sleeves. This gives : 2 large crates, 3 small boxes, and 18 sleeves.
The second packing does not satisfy the final condition because 3 small boxes is not more than 18 sleeves. The first packing does satisfy it because .
Therefore Nurse Joy uses 1 large crate, 14 small boxes, and 8 one-ball sleeves.
Why this is the only answer
Nurse Joy can use at most 2 large crates because 3 crates would already hold 300 balls. Checking 0, 1, and 2 large crates while keeping exactly 23 total containers gives no valid packing with 0 crates, , and . These cases cover every possible number of large crates, and only the middle case has more boxes than sleeves.
Check
The selected packing contains Poké Balls. It uses full containers, and . Every condition is satisfied.
Technical fit and rating
Number and operations
How the rating works →mathjewels.com/answers/problems/9/