Problem 6 · 2007 AMC 8
Easy
Fractions, Decimals & Percents
percent-decrease
The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 7 cents per minute. Find the approximate percent decrease in the cost per minute of a long-distance call.
Show answer
Answer: E — About 80%.
Show hints
Hint 1 of 2
Percent decrease compares the drop to where you started, not where you ended — the 41 is the reference, not the 7. And the answers are far apart, so a rough estimate is enough.
Still stuck? Show hint 2 →
Hint 2 of 2
Percent change = (change) ÷ (original). The original is always the denominator.
Show solution
Approach: drop over the starting value, estimated
- The drop is 41 − 7 = 34, measured against the starting price 41 (not the ending 7).
- 34/41 is just under 34/40, and 34 is most of 41 — clearly in the 80s percent, so 80%.
- Common trap: dividing by the new value (7) instead of the original (41) inflates the answer. Decrease always references the start.
Another way — the price almost vanished:
- 7 cents is roughly one-sixth of 41 cents, so about 5/6 of the cost disappeared.
- 5/6 ≈ 83%, and the nearest choice is 80%.
Mark:
· log in to save