My basketball team plays three games per week. During the first four weeks, we lost all $12$ of our games. During week $5,$ we won two games and lost one game, bringing us to two wins and $13$ losses for the season so far. Each week after that, we won two games and lost one game. At the end of which week will my team have won at least $60\%$ of its games total for the first time in the season?
Call the number of additional weeks after the first five = W
And 15 total games have been played during the first five weeks = 13 + 2 =15
The number of total games past week 5 = 3W
And the number of total wins past week 5 = 2W
So.....we want to solve this
2 + 2W
________ = .60 multiply both sides by 13 + 3W
15 + 3W
2 + 2W = .60 ( 15 + 3W) simplify
2 + 2W = 9 + 1.8W subtract 1.8W, 2 from both sides
.2W = 7 divide both sides by .2
W = 35
So.... 60% of the games will be won after week (5 + 35) = 40
Check.....after 40 weeks 2 + 2(35) = 72 games will have been won
And 15 + 3(35) = 120 games would have been played
So 72 /120 = .60 = 60%