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# A basketball team scored x points per game in its first n games of the

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Math Expert
Joined: 02 Sep 2009
Posts: 58442
A basketball team scored x points per game in its first n games of the  [#permalink]

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31 Oct 2016, 03:08
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Difficulty:

25% (medium)

Question Stats:

69% (01:31) correct 31% (01:50) wrong based on 102 sessions

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A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 3 games?

A. x + 3y/(n + 3)
B. x + y/(n + 3)
C. (x + 3y)/(n + 3)
D. (nx + 3y)/(n + 3)
E. (3x + ny)/(n + 3)

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Re: A basketball team scored x points per game in its first n games of the  [#permalink]

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31 Oct 2016, 03:56
Points scored in the first n games = n * x
Points scored in the next 3 games = 3 * y
Total points scored = nx+3y
Average = Total Points/ Number of Games
= $$\frac{(nx +3y)}{(n+3)}$$
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Re: A basketball team scored x points per game in its first n games of the  [#permalink]

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31 Oct 2016, 08:00
Bunuel wrote:
A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 3 games?

A. x + 3y/(n + 3)
B. x + y/(n + 3)
C. (x + 3y)/(n + 3)
D. (nx + 3y)/(n + 3)
E. (3x + ny)/(n + 3)

Total points in first n games = nx
Total marks in next 3 games is 3y

So, Average marks in n + 3 games = $$\frac{(nx + 3y)}{( n + 3)}$$

Hence, correct answer will be (D)

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Re: A basketball team scored x points per game in its first n games of the  [#permalink]

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29 Aug 2018, 17:43
This is my thought process.
First, lets organize the information at hand.
X = the average points per first n games
N = the first # of games played
Y = the average points per game after the first N games
3 = games after N, so this is Y
Objective, What is the average points per game for x + y games?

Ok, so we need to get an average of points. What do we do to get an average number of something? Its total points/number of games played (which we already have! n + 3). So we just need to figure out the numerator.
We can get the total points by multiplying the number of games n and the average points per first n games, which is x, and all games after the N games, i.e. 3 games, multiply that with the average points per game after the first N games, which is y.

Looking like (nx + 3y)/ (n + 3)

Re: A basketball team scored x points per game in its first n games of the   [#permalink] 29 Aug 2018, 17:43
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