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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 $26$ games out of $49$ games they have played. How many home games has Lisa's team played?

 May 3, 2015

Best Answer 

 #1
avatar+99377 
+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.

 May 4, 2015
 #1
avatar+99377 
+16
Best Answer

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

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