Problem 1 worked answer
The Museum Display
Designed for Grade 3 · Uses Middle Grade 3 math · About 5–12 minutes
Earn one jewelRose-Cut DiamondLevel 3
At a glance
- The only working choice is 2 sapphire cases.
- That choice leaves 25 jewels, so each tray receives 5 jewels.
Key idea
If (s) cases receive sapphires, the finished total is (24+3s-5=19+3s). Test the complete bounded set (s=0,1,\ldots,6); a choice works exactly when this total is divisible by 5.
Test every possible choice
Six cases with 4 rubies in each case always contain
rubies.
For each possible (s), the remaining total is (19+3s):
| Sapphire cases (s) | Jewels left | Divisible by 5? |
|---|---|---|
| 0 | 19 | No |
| 1 | 22 | No |
| 2 | 25 | Yes |
| 3 | 28 | No |
| 4 | 31 | No |
| 5 | 34 | No |
| 6 | 37 | No |
When (s=2), (25\div5=5), so every tray receives 5 jewels.
Check
The table includes every allowed whole-number choice from 0 through 6, so no case has been skipped. Only 25 is a multiple of 5. Multiplication checks the working share: , and .
Technical fit and rating
MJ 3.4 · C3 · W2
Stretch challenge · Moderate workload
Number and operations
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