In a soccer game the winner gains 3 points, while the loser gains 0 points. If the game is a draw, then the two teams gain 1 point each. A team has played 38 games gaining 80 points. Find the greatest possible number of games that the team lost.

10 losses

Step-by-step explanation:

Here, we want to get the greatest possible number of games the team lost

Let the number of games won be x

Number drawn be y

Number lost be z

Mathematically;

x + y + z = 38

Let’s now work with the points

3(x) + 1(y) + z(0) = 80

3x + y = 80

So we have two equations here;

x + y + z = 80

3x + y = 80

The greatest possible number of games lost will minimize both the number of games won and the number of games drawn

We can have the following possible combinations of draws and wins;

26-2

25-5

24-8

23-11

22-14

21-17

21-17 is the highest possible to give a loss of zero

Subtracting each sum from 38, we have the following loses:

10, 8, 6, 4, 2 and 0

This shows the greatest possible number of games lost is 10

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8

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