Question

A team has won 50% of the 60 games it played, find the number of games the team must win in succession to increase its winning percentage to 60%?

Answer 1

50 % = 50 / 100 = 0.5

A team won 0.5 * 60 = 30 games

x = the number of games the team must win


60 % = 60 / 100 = 0.6

Proportion :

( 30 + x ) / ( 60 + x ) = 0.6 Multiply both sides by 60 + x

30 + x = ( 60 + x ) * 0.6

30 + x = 36 + 0.6 x Subtract 30 to both sides

30 + x - 30 = 36 + 0.6 x - 30

x = 6 + 0.6 x Subtract 0.6 x to both sides

x - 0.6 x = 6

0.4 x = 6 Divide both sides by 0.4

x = 6 / 0.4 = 60 / 4 = 15


Proof :

( 30 + 15 ) / ( 60 + 15 ) = 45 / 75 =

( 3 * 5 * 3 ) / ( 3 * 5 * 5 ) =

3 / 5 = 0.6 = 60 %