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Math Expert V
Joined: 02 Sep 2009
Posts: 58398
A soccer team scores x goals the first game then averages twice as man  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 79% (02:07) correct 21% (02:21) wrong based on 18 sessions

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A soccer team scores x goals the first game then averages twice as many goals for the next 5 games. The team averages two goals less than the average (arithmetic mean) of the previous 5 games over their next four games. How many goals will the team have scored after 10 games?

A. 19x − 8
B. 15x
C. 12x
D. 19x/10
E. 27x

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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3571
A soccer team scores x goals the first game then averages twice as man  [#permalink]

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Bunuel wrote:
A soccer team scores x goals the first game then averages twice as many goals for the next 5 games. The team averages two goals less than the average (arithmetic mean) of the previous 5 games over their next four games. How many goals will the team have scored after 10 games?

A. 19x − 8
B. 15x
C. 12x
D. 19x/10
E. 27x

Attachment: soccergoals.png [ 11.82 KiB | Viewed 371 times ]

Algebra
There are three groups of games.
Each group has
• A, an average number of goals
• n, a number of games and
• S, Sum (A * n), total number of goals for that group

There are 1 + 5 + 4 = 10 games
Total number of goals? Sum the sums for each group

$$A*n = S$$
1) first game: team scores x goals
A = x, n = 1, S = x

2) next 5: average is twice that of first game
A = 2x, n = 5, S = 10x

3) next 4: 2 goals less than average for the previous 5 games
A = 2x - 2, n = 4
S = 4(2x - 2) = 8x - 8

The total number of goals after 10 games: sum the sums
$$x + 10x + 8x - 8$$ =

$$19x - 8$$

Assign values

• Let first week = 1 goal
1 game * average of 1 goal = 1 goal total

• Next 5 weeks, team averages twice as many goals as the first week

5 games * average of 2 goals = 10 goals

• Next 4 weeks, team averages 2 less than average (arithmetic mean) of previous 5 games' average

4 games * average of 0 goals = 0 goals total

• Total number of goals scored after 10 games?

Number of games? 1 + 5 + 4 = 10
Total number of goals: (1 + 10 + 0) = 11 goals total

• Using x = 1, find the answer choice that yields 11 goals
Eliminate D (not an integer) and E immediately (it's huge)

A. 19x − 8: (19)(1) - 8 = 11. MATCH

B. 15x: (15)(1) = 15. NOT A MATCH

C. 12x (12)(1) = 12. NOT A MATCH

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Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver A soccer team scores x goals the first game then averages twice as man   [#permalink] 02 Jan 2018, 15:10
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