AMC 10 · 2015 · #5
Grade 6 arithmeticPick an answer.
AMC 10 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
An average hides the total, so Tool #7 (Identify Subproblems) splits the work into clean pieces: first turn each average back into a sum of points, once for the 14 tests and once for all 15. Tool #11 (Work Backwards) then recovers the single missing number — Payton's score is whatever was added to the old total to make the new total, so subtract the two sums.
Total of the 14 graded tests
The 14 graded tests average 80, so their total is 14 × 80 = 1120 points.
An average is just the total shared out evenly, so multiplying it back by the count rebuilds the total.
6.SP.B.5Identify SubproblemsTotal of all 15 tests
With Payton's test included, all 15 average 81, so the total is 15 × 81 = 1215.
The same total = average × count rule turns the new average into the new full total.
5.NBT.B.5Identify SubproblemsSubtract to find Payton's score
Payton's score is the gap between the totals: 1215 − 1120 = 95, choice (E).
Adding one score raises the total by exactly that score, so the rise in the total is the score itself.
4.NBT.B.4Work BackwardsTurn each average back into a total by multiplying by the count, then the score you added is just the jump in the total.
- Total of the 14 graded tests
- Total of all 15 tests
- Subtract to find Payton's score
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Same archetype — closest grade level first.
