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?

AWESOMEEE
May 3, 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

#1**+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