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
A football team averaged 35 points per game over the first
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$$? = n + 1$$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
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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Say the team played n games before the final game.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
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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This is a weighted average/mixture problem.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
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:
https://www.beatthegmat.com/ratios-fract ... 15365.html
https://www.beatthegmat.com/mean-t266852.html#684151
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Let n be the number of games the team played before the final game. We can create the equation: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
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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