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Over the first x games of his basketball season, Martin averaged 32 po

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Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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New post 16 Feb 2017, 00:41
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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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Re: Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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New post 16 Feb 2017, 01:04
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ziyuenlau wrote:
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


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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Re: Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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New post 16 Feb 2017, 03:27
ziyuenlau wrote:
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



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  [#permalink]

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New post 16 Feb 2017, 11:43
ziyuenlau wrote:
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


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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Re: Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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New post 28 Jan 2019, 05:01
hazelnut wrote:
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


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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Re: Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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New post 18 Jun 2019, 07:45
1
hazelnut wrote:
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


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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Re: Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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New post 21 Jun 2019, 19:49
hazelnut wrote:
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


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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Re: Over the first x games of his basketball season, Martin averaged 32 po   [#permalink] 21 Jun 2019, 19:49
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