Question

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?

Explain how you solved the problem.

Answer 1

The team has played 24 home games.
Let h be the number of home games and a be the number of away games.  The total number of games is 49; this gives ush+a=49
They won 2/3 of the home games and 2/5 of the away games; there were 26 games won.  This gives us2/3h + 2/5a = 26
In the first equation we isolate h by subtracting a from both sides:h+a-a=49-ah=49-a
Substitute this into the second equation:2/3(49-a)+2/5a = 26
Using the distributive property, we have2/3*49 - 2/3*a + 2/5a = 2698/3 - 2/3a + 2/5a = 26
Finding a common denominator to combine like terms, we have98/3 - 10/15a + 6/15a = 2698/3 - 4/15a = 26
We want to convert the whole number to thirds as well; 26 = 26*3/3 = 78/3:98/3 - 4/15a = 78/3
Subtracting 98/3 from both sides:98/3 - 4/15a - 98/3 = 78/3 - 98/3-4/15a = -20/3
Divide both sides by -4/15:a = -20/3 ÷ -4/15a = -20/3 × - 15/4 = 300/12 = 25
There were 25 away games.
This means there were 49-25 = 24 home games.