A football team averaged 35 points per game over the first

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.

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.

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.

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