Question

This season, Lisa's lacrosse team has won 2/3 of their home games (games played at Lisa's school), but just 2/5 of their away games (games played at other schools). In total, Lisa's team has won 26 games out of 49 games they have played. How many home games has Lisa's team played? Explain how you solved the problem.

Answer 1

Let X be the at home games and Y be the away games

then  

X+Y=49     (1)      

and

(2x/3 + 2y/5)=26

15(2x/3 + 2y/5)=15*26

(15*2x/3) + (15*2y/5)=390

5*2x + 3*2y=390

10x + 6y=390

5x + 3y=195      (2)

3X+3Y=147        3*(1)          (1b)

(2)-(1b)

2X=48

X=24

X+Y=49

24+Y=49

Y=49-24

y=25

24 home games      25 away games.