Answer: 4 ties or draws
8 wins, 4 ties, 20 losses
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Explanation:
The ratio 2:1:5 is of the format wins:ties:losses where getting a draw is the same as getting a tie.
So one possibility is that they won 2 matches, tied once, and lost 5 matches. The only problem is that it doesn't fit with the statement that "The team lost 12 more matches than they won."
We could guess-and-check our way to the answer, but I think using algebra is the most efficient route.
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Let x = number of ties
2x = number of wins and 5x = number of losses
Note the ratio 2x:x:5x reduces to 2:1:5 after dividing everything by x.
Since the team lost 12 more matches than they won, this means,
loss count = (win count) + 12
5x = (2x) + 12
5x-2x = 12
3x = 12
x = 12/3
x = 4
The team tied 4 times and has 2x = 2*4 = 8 wins and 5x = 5*4 = 20 losses.
The ratio 8:4:20 reduces to 2:1:5 when you divide all parts by the GCF 4.
Also, the gap between 8 wins and 20 losses is 20-8 = 12 to help fully confirm we have the correct answer.
