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? Explain how you solved the problem.
1 answer:
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 us h+a=49 They won 2/3 of the home games and 2/5 of the away games; there were 26 games won. This gives us 2/3h + 2/5a = 26 In the first equation we isolate h by subtracting a from both sides: h+a-a=49-a h=49-a Substitute this into the second equation: 2/3(49-a)+2/5a = 26 Using the distributive property, we have 2/3*49 - 2/3*a + 2/5a = 26 98/3 - 2/3a + 2/5a = 26 Finding a common denominator to combine like terms, we have 98/3 - 10/15a + 6/15a = 26 98/3 - 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 ÷ -4/15 a = -20/3 × - 15/4 = 300/12 = 25 There were 25 away games. This means there were 49-25 = 24 home games.
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