AMC 10 · 2023 · #1
Grade 5 rate-ratioPick an answer.
The easier problem hiding inside is just averaging: if all the juice were pooled and shared equally among 4 identical glasses, how much would each glass get? Tool #9 reframes the whole pouring scene as "find the average level". Once we know the target level, Tool #11 (Work Backwards) finishes: each full glass must drop from 1 to that target, and the amount poured out is the difference. A quick Tool #1 sketch of four bar-glasses makes the conservation visible without algebra.
Find the total
The total never changes.
Adding 1 three times and then 1/3 is just adding fractions with the same denominator — a Grade 5 skill.
5.NF.A.1Solve An Easier Related ProblemFind the target per glass
Dividing by four gives the target.
Sharing a total equally among 4 groups is just dividing a fraction by a whole number.
Sharing a total equally among four glasses means each glass gets one quarter of it.
▸ Why?
A quarter is one of four equal shares, so equal sharing is exactly that fraction.
▸ Why?
The juice is exactly the four glasses put together, so the total is what gets shared.
Find how much leaves
What leaves a full glass is the answer.
If you know the start (1) and the end (5/6), the missing piece is just the subtraction 1 - 5/6.
5.NF.A.1Work BackwardsCheck it
Checking confirms one sixth.
A picture of four equal bars at height 5/6 confirms the pouring distributes correctly.
5.NF.A.2Draw A DiagramThis AMC 12 problem only needs Grade 5 fraction-sharing you already know — pool all the juice, divide by 4, and pour out the leftover above that target.