2) is a little difficult
At the end of Week 5 of my basketball team's season, our record is 3 wins and 17 losses. Each week after that, we win 3 games and lose 1 game. At the end of which week will my team have won at least 65% of its games total for the first time in the season?
Call the number of additional weeks (past week 5) that it takes to win 65% of the games, W
Our team plays 4 games per week and we win 3 of these
So
Total games won
________________ = .65
Total games played
3 + 3 W
____________ = .65
(17 + 3) + 4W
3 + 3 W
________ = .65 multiply both sides by 20 + 4W
20 + 4W
3 + 3 W = .65 ( 20 + 4 W ) simplify
3 + 3 W = 13 + 2.6 W subtract 2.6 W, 3 from both sides
.4W = 10 divide both sides by .4
W = 25 (additional weeks past week 5 ) ....so ...after the 30th week
Check
3 + 25(3) 78
__________ = ____ = .65 !!!!
20 + 25 (4) 120