Problem 4 worked answer
The Chest Room Split
Designed for Grade 3 · Uses Middle Grade 3 math · About 3–7 minutes
At a glance
- Part 1: Each chest contains 8 iron pieces.
- Part 2: Alex must open 3 chests, and 6 pieces remain in the third chest after she collects 18.
1. Find the equal share
The 48 pieces are shared equally among 6 chests:
.
Therefore each chest contains 8 iron pieces.
2. Find the fewest chests
Alex empties a chest before opening another. Two complete chests provide
pieces.
Sixteen is less than the 18 pieces she needs, so 2 chests are not enough. She must open a third chest. After taking all 16 pieces from the first two chests, she still needs
pieces.
The third chest begins with 8 pieces. Alex takes 2, leaving
pieces.
Thus the fewest possible number is 3 chests, with 6 pieces remaining in the last chest she opens.
Why three is the minimum
The comparison covers both sides of the claim: 2 chests supply only 16 pieces and cannot work, while opening a third chest supplies enough. Therefore no smaller number of chests can collect 18 pieces.
Check
The equal share checks by multiplication: . The collection also checks: , and the third chest is accounted for because .
Technical fit and rating
Number and operations
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