Question

E) Over a season a football team won, drew and lost matches in the ratio 2:1:5.

Answer 1

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.