Question

his 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

24 Home games

Explanation:

let
`x` denote the number of home games played, and
`y` denote the number of home games played. We are given the total number of games played as 49

and total wins as 26.

The problem can be expressed in equation form as:
`(2)/(3)x+(2)/(5)y=26`...
`eqtn1`

Total games is expressed as
`x+y=49`...
`eqtn2`

Rewrite equation 1 to remove fractions:

`(2)/(3)x+(2)/(5)y=26\\=>5x+3y=195\\`

Solve for x to obtain total home games played.

Making
`x` the subject in eqtn 2:

`x=49-y`

Substitute for
`x` in eqtn1:

=>

`5(49-y)+3y=195\\-5y+3y=195-245\\-2y=-50\\y=25`

To obtain
`x`, replace y value in eqtn2:

`x+y=49\\y=25\\Therefore\\x=49-25\\x=24`

Home games played is 24