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Over the first x games of his basketball season, Martin averaged 32 po 16 Feb 2017, 00:41
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69% (01:24) correct 31% (01:39) wrong based on 713 sessions

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Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
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B
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Over the first x games of his basketball season, Martin averaged 32 po 16 Feb 2017, 01:04
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ziyuenlau
Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
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Hi

\(g_i\) = score per particular game

\(\frac{g_1 + g_2 + g_3 + ... + g_x}{x} = 32\)

\(g_1 + g_2 + g_3 + ... + g_x = 32x\)

and

\(g_1 + g_2 + g_3 + ... + g_x + 14 = 30(x + 1)\)

\(32x + 14 = 30(x + 1)\)

\(2x = 16\)

\(x = 8\)

total \(x+1\) games ----> \(8 + 1 = 9\)

Answer B
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Over the first x games of his basketball season, Martin averaged 32 po 16 Feb 2017, 03:27
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ziyuenlau
Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
Show more


Hi

Two other simpler ways..
1) 2 points drop is equal to difference between 14 to 32.
So 2(x+1)=32-14..
2x+2=18.... x=16/2.... x=8...
X+1=8+1=9..

2) weighted average..
\(\frac{32-30}{30-14}=\frac{1}{x}\)....
\(\frac{2}{16}=\frac{1}{x}\)..
x=8..
Ans x+1=9
B
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Over the first x games of his basketball season, Martin averaged 32 po 16 Feb 2017, 11:43
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ziyuenlau
Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
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let p=total points in x games
p=32x
substituting,
(32x+14)/(x+1)=30
x=8
x+1=9
B
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Over the first x games of his basketball season, Martin averaged 32 po 28 Jan 2019, 05:01
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hazelnut
Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
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How many games were played that season

Total number of points = n
Number of games = x

Average = Total number of points/Number of games

n/x = 32

n = 32x

n+14 / x+1 = 30

n+14 = 30x + 30
32-30x = 16
2x = 16
x = 8

Total number of games x+1 = 8 + 1 = 9

Answer B
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Over the first x games of his basketball season, Martin averaged 32 po 18 Jun 2019, 07:45
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hazelnut
Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
Show more

Since the seasonal average = 30 points per game, the total number of points must be a MULTIPLE OF 30.

Over the first x games of his basketball season, Martin averaged 32 points per game.
In his last game, he scored 14 points.
Implication:
32x + 14 = MULTIPLE OF 30
32x = (MULTIPLE OF 30) - 14
32x = INTEGER WITH A UNITS DIGIT OF 6

The answer choices represent the value of x+1, implying the following options for x:
A. 7
B. 8
C. 9
D. 10
E. 11

Since 32x must yield a units digit of 6, only B is viable,

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B
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Over the first x games of his basketball season, Martin averaged 32 po 21 Jun 2019, 19:49
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hazelnut
Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
Show more

We can create the equation:

30 = (32x + 14)/(x + 1)

30x + 30 = 32x + 14

16 = 2x

8 = x

Since he actually played x + 1 games during the season, he played 9 games during the season.

Answer: B
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Over the first x games of his basketball season, Martin averaged 32 po 17 Feb 2024, 07:53
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BillyZ
Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

A. 8
B. 9
C. 10
D. 11
E. 12
Show more
­Total score in x games is 32x

Now, \(\frac{32x + 14}{(x +1)} = 30\)

Thus, \(32x + 14 = 30x + 30\)

Or, \(2x = 16\)

Or, \(x = 8\)

Total games played is \(8 + 1 = 9\), Answer must be (B)
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Over the first x games of his basketball season, Martin averaged 32 po 17 Aug 2025, 02:06
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Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points and his average dropped to 30 points per game for the x+1 game season. How many games were played that season?

--> We can treat all the points in x games as 32. 32 32 32 ... x times
Now if he plays another match and score 14, this will bring the avg. down.

32-14 = 18 so the last game “pulled down” the overall average by the 18-point shortage.
Since the avg dropped by 2 points.
Each of the x+1 games had its average decreased by 2 → total decrease = 2(x+1) points.

2(x+1)=18
x+1=9
Hence the total no. of matches played= 9
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