+1314 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 
games out of 
games they have played. How many home games has Lisa's team played?
+118724 Let X be the at home games and Y be the away games
then
X+Y=49 (1)
and
$$\\\frac{2X}{3}+\frac{2Y}{5}=26\\\\
15\left(\frac{2X}{3}+\frac{2Y}{5}\right)=15*26\\\\
\frac{15*2X}{3}+\frac{15*2Y}{5}=15*26\\\\
10X+6Y=390\\\\
5X+3Y=195\qquad(2)\\\\$$
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.
+118724 Let X be the at home games and Y be the away games
then
X+Y=49 (1)
and
$$\\\frac{2X}{3}+\frac{2Y}{5}=26\\\\
15\left(\frac{2X}{3}+\frac{2Y}{5}\right)=15*26\\\\
\frac{15*2X}{3}+\frac{15*2Y}{5}=15*26\\\\
10X+6Y=390\\\\
5X+3Y=195\qquad(2)\\\\$$
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.
