A team has won 60 percent of the games it has played so far. If the team wins the 15 remaining games in the season, it will have won 80 percent of the season's games. How many games will the team play over the entire season?

Answer 1

60 % = 60 / 100 = 0.6

80 % = 80 / 100 = 0.8

x = Number of games in season

A team has played so far x - 15 games and won 60 % of the games .

So :

0.6 * ( x - 15 ) + 15 = 0.8 x

0.6 x - 0.6 * 15 + 15 = 0.8 x

0.6 x - 9 + 15 = 0.8 x

0.6 x + 6 = 0.8 x Subtract 0.6 x to both sides

0.6 x - 0.6 x+ 6 = 0.8 x - 0.6 x

6 = 0.2 x Divide both sides by 0.2

6 / 0.2 = 0.2 x / 0.2

30 = x

x = 30

Proof :

A team has played so far x - 15 = 30 - 15 = 15 games

A team has won 0.6 * 15 = 9 games

If the team wins the 15 remaining games in the season, it will have 9 + 15 = 24 won games

24 / 30 = 0.8 = 0.8 * 100 / 100 = 80 / 100 = 80 %