Problem 10 · 2023 Math Kangaroo
Medium
Fractions, Decimals & Percents
percent-multiplier
After playing 200 games of chess, Beth’s winning rate is exactly 49 %. What is the minimum number of games she has to still play to increase her winning rate to 50 %?
Show answer
Answer: D — 4
Show hints
Hint 1 of 2
She has 98 wins out of 200; adding x more wins makes it (98+x)/(200+x).
Still stuck? Show hint 2 →
Hint 2 of 2
Set that fraction to at least 1/2 and solve for the smallest whole x.
Show solution
Approach: set up the win-rate inequality
- 49% of 200 is 98 wins.
- Winning the next x games gives rate (98+x)/(200+x).
- Require (98+x)/(200+x) ≥ 1/2: 196+2x ≥ 200+x, so x ≥ 4.
- The minimum is 4 games.
Mark:
· log in to save