Solitare
After playing 500 games, my success rate at Solitare is 49%. How many games do I need to win to increase my success rate to 50%?
Age
14 to 16
Challenge level
Problem
After playing $500$ games, my success rate at Solitaire is $49\%$.
Assuming I win every game from now on, how many extra games do I need to play in order to increase my success rate to $50\%$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 10 more games
The number of games lost
$49\%\times500 = 250-5 = 245$ games won
$\therefore 255$ games lost
Win more games $\therefore$ number of games lost is still $255$
$50\%$ win means $50\%$ loss so $255=50\%$ of total number of games
$255\times2 = 510$ which is $10$ more than $500$
Using balance
$500\times49\%\qquad+\qquad? \times100\%$ has an average of $50\%$
$\nearrow$ $\nearrow$
$1\%$ from $50\%$ $50\%$ from $50\%$
$\uparrow$ $\uparrow$
Need $50$ times more of these than of these
So $50$ times fewer than $500$
$500\div50=10$
$10$ more games