Question

Can someone help me with this Question.

Answer 1

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

• 
  `P=3W+D`

A) First, we can start by analyzing the first premise. The team has
`8` wins and
`5` losses. It earned
`8 * 3 = 24` points in total from the matches it won and
`1*5=5` points in total from the matches it drew. Therefore, it earned
`24+5=29` points.

B) After
`39` matches, the team managed to earn
`54` points in total.
`12` of these matches have ended in draws. Therefore, this team has won and lost a total of
`39-12=27` matches. This number includes all matches won and lost. In total, the team earned
`12*1=12` points from the
`12` matches that ended in a draw.

`54-12=42` points is the points earned after
`27` matches. By dividing
`42` by
`3` ( because
`3` points is the score obtained as a result of the matches won), we find how many matches team won.
`42/3=14` matches won.

That leaves
`27-14=13` matches. These represent the matches team lost.

Finally, the answers are below.

`A)29`

`B)13`

Answer 2

a) 29 points

b) 13 losses

Explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

A 8 wins, 5 draws

The number of points the team has is ...

P = 3W +D

P = 3(8) +(5) = 29

The team has 29 points.

B 54 points

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

P = 3W +D

54 = 3W +12

42 = 3W

14 = W

Then the number of losses is ...

W +D +L = 39

14 +12 +L = 39 . . . substitute the known values

L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

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Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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