Problem 9 · 2010 AMC 8
Easy
Fractions, Decimals & Percents
weighted-average
Ryan got 80% of the problems correct on a 25-problem test, 90% on a 40-problem test, and 70% on a 10-problem test. What percent of all the problems did Ryan answer correctly?
Show answer
Answer: D — 84%.
Show hints
Hint 1 of 2
You can't just average 80, 90, 70 — the tests are different sizes, and the big test should pull harder. Go back to raw counts: how many problems did he actually get right out of how many total?
Still stuck? Show hint 2 →
Hint 2 of 2
An overall percent is a weighted average: total correct over total problems. Each test's weight is its number of problems.
Show solution
Approach: weighted average via raw counts
- Ignore the percents for a moment and count right answers: 0.8 · 25 + 0.9 · 40 + 0.7 · 10 = 20 + 36 + 7 = 63 correct.
- Out of 25 + 40 + 10 = 75 problems: 63 / 75 = 84%.
- Sanity check: 84 lands between the lowest (70) and highest (90) scores and leans toward 90 — right, because the 40-problem test is the heaviest. A plain average of 80, 90, 70 gives 80, the wrong answer (A is the trap), proof that size matters.
Mark:
· log in to save