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A football team averaged 35 points per game over the first

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A football team averaged 35 points per game over the first

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A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12

OA C

Source: Veritas Prep

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BTGmoderatorDC wrote:
A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12
Let n be the number of games the team played before the final game. We can create the equation:

34 = (35n + 28)/(n + 1)

34n + 34 = 35n + 28

6 = n

So the team played n + 1 = 7 games.

Answer: C

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BTGmoderatorDC wrote:
A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12
This is a weighted average/mixture problem.

Average score for the first N games = 35.
Score for the final game = 28.
Average score for the MIXTURE of all the games = 34.

Step-by-step instruction for the alligation approach:

Step 1: Plot the 3 averages on a number line, with the average for the first N games and that for the final game on the ends and the average for the mixture in the middle.
N 35----------------34----------------28 F

Step 2: Calculate the distances between the averages.
N 35--------1-------34--------6------28 F

Step 3: Determine the ratio in the mixture.
The ratio of N to F is equal to the RECIPROCAL of the distances in red.
N:F= 6:1

Since N:F = 6:1, the team played N=6 games with an average score of 35 and 1 final game with a score of 28, for a total of 7 games.

The correct answer is C.

Similar problems:

http://www.beatthegmat.com/ratios-fraction-problem-t115365.html
https://www.beatthegmat.com/mean-t266852.html#684151

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BTGmoderatorDC wrote:
A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12
Source: Veritas Prep
$$? = n + 1$$
Let´s do it using alligation:




$${1 \over {n + 1}} = {{35 - 34} \over {35 - 28}} = {1 \over 7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = n + 1 = 7$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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BTGmoderatorDC wrote:
A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12

OA C

Source: Veritas Prep
Say the team played n games before the final game.

Total points scored in n games = 35n
Total points scored in (n + 1) games, incl. final game = 35n + 28

=> Average score of (n + 1 ) games = (35n + 28) / (n + 1)

(35n + 28) / (n + 1) = 34 (given)

=> n = 6 => n + 1 = 7.

The correct answer: C

Hope this helps!

-Jay
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35*n . . . sum of the points of the first n games.
n + 1 . . . total number of games

34 = (35*n + 28)/(n + 1)
34n + 34 = 35n + 28
n = 34 - 28 = 6
n + 1 = 7

Therefore, C is the correct answer.

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