Question

This season, Lisa's lacrosse team has won $\frac 23 of their home games (games played at Lisa's school), but just $\frac 25 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?

Answer 1

Answer:

Lisa's team have played 24 home games and 25 away games.

Step-by-step explanation:

Given:

Let $x$ represents games played at home.

also $y$ represent games played away.

Total number of games played = 49

∴ $x+y=49 \ \ \ \ equation \ 1$

Now according to given data:

Number of home games won = $\frac{2}{3}$

Number of away game won = $\frac{2}{5}$

Total games won =26

Hence

$\frac{2}{3}x+\frac{2}{5}y=26\\\\\frac{2\times 5}{3\times 5}x+\frac{2\times 3}{5\times 5}y=26\\\\\frac{10}{15}x+\frac{6}{15}y=26\\\\\frac{10x+6y}{15}=26\\\\10x+6y= 26\times 15\\10x+6y = 390\\2(5x+3y)=390\\5x+3y=\frac{390}{5}\\\\5x+3y=195 \ \ \ \ equation \ 2$

Now multiplying equation 1 by 3 we get,

$3(x+y)=3\times49\\3x+3y=147 \ \ \ \ \ equation \ 3$

Now Subtracting equation 2 by equation 3 we get,

$(5x+3y=195)-(3x+3y=147)\\2x=48\\x= \frac{48}{2}=24$

Substituting value of x in equation 1 we get.

$x+y=49\\24+y=49\\y=49-24=25$

Hence Lisa's team have played 24 home games and 25 away games.