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# 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 game

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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?

May 3, 2015

#1
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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.

May 4, 2015

#1
+16

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.

Melody May 4, 2015