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# The average (arithmetic mean) number of points per game scored by a

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Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
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The average (arithmetic mean) number of points per game scored by a  [#permalink]

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26 Mar 2019, 10:44
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Difficulty:

25% (medium)

Question Stats:

74% (01:47) correct 26% (02:48) wrong based on 35 sessions

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The average (arithmetic mean) number of points per game scored by a football team during the first x games of a season was 17. The average number of points scored by the team in the remaining y games of the season was 29. If the average number of points scored by the team over the entire season was 21, what is the ratio of x to y?

A) 1:2
B) 17:21
C) 17:29
D) 2:1
E) 5:2
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Re: The average (arithmetic mean) number of points per game scored by a  [#permalink]

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26 Mar 2019, 15:57
It's a weighted average problem. Draw the three averages on a number line:

--17----21------------29--

The ratio of the distances to the middle will equal the ratio of the two parts of the season. So the numbers of games in the two parts of the season are in a 4 to 8, or 1 to 2 ratio, and since 21 is closer to 17, x is larger than y, so the ratio of x to y is 2 to 1.
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Re: The average (arithmetic mean) number of points per game scored by a  [#permalink]

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28 Mar 2019, 06:29
energetics wrote:
The average (arithmetic mean) number of points per game scored by a football team during the first x games of a season was 17. The average number of points scored by the team in the remaining y games of the season was 29. If the average number of points scored by the team over the entire season was 21, what is the ratio of x to y?

A) 1:2
B) 17:21
C) 17:29
D) 2:1
E) 5:2

We can create the equation:

(17x + 29y)/(x + y) = 21

17x + 29y = 21x + 21y

8y = 4x

8/4 = x/y

2/1 = x/y

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Re: The average (arithmetic mean) number of points per game scored by a   [#permalink] 28 Mar 2019, 06:29
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