AMC 10 · 2011 · #2
Grade 6 arithmeticPick an answer.
The goal is stated in terms of the final average, and we must recover a single missing score. Tool #11 (Work Backwards) runs the average formula in reverse: from the target average, find the total the six tests must reach, then subtract what she already has. Tool #7 (Identify Subproblems) splits the job into current-average, target-total, and needed-score. Tool #3 (Eliminate Possibilities) uses the answer choices to confirm that anything below 95 falls short.
Find the current average
The current average is 77.
An average is just the total shared equally across all the tests.
6.SP.B.5Identify SubproblemsSet the target average
The target average is 80.
The lowest passing score comes from just barely reaching the target, not overshooting it.
6.EE.B.5Work BackwardsWork backwards to the six-test total
That fixes a new total over six tests.
If the average must be 80 over six tests, the points must pile up to 80 six times over.
If the average must be a certain value over six tests, the points have to pile up to that value six times over.
▸ Why?
An average is a total shared out over a count, so multiplying it back by the count returns the total.
▸ Why?
That total is the individual scores added together, so the missing one is the leftover.
Subtract to find the needed score
Subtracting gives 95, choice (E).
The missing score is exactly the leftover distance between what she has and the total she needs.
4.OA.A.3Eliminate PossibilitiesTo find one missing score for a target average, figure out the total all the tests must reach, then subtract the points you already have.
- Find the current average
- Set the target average
- Work backwards to the six-test total
- Subtract to find the needed score