Question 822025
The winning percentage is found using an equation like:
<pre>
                         number of wins
Winning percentage = --------------------- * 100
                     total number of games
</pre>Let x = the number of consecutive games to win to reach a winning percentage of 60%. Then...
42 + x = the total number of wins
42 + 36 + x = the total number of games.
This makes our equation:
{{{60 = (42+x)/(42+36+x) * 100}}}
which simplifies to:
{{{60 = (42+x)/(78+x) * 100}}}
Dividing each side by 100:
{{{0.60 = (42+x)/(78+x)}}}
Multiplying each side by (78+x) (to eliminate the fraction):
{{{0.60(78+x) = 42+x}}}
Simplifying:
{{{46.8 + 0.60x = 42+x}}}
Subtracting 0.60x:
{{{46.8 = 42 + 0.40x}}}
Subtracting 42:
{{{4.8 = 0.40x}}}
Dividing by 0.40:
{{{12 = x}}}