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

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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1323
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Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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15 Feb 2017, 23:41
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Difficulty:

45% (medium)

Question Stats:

60% (01:30) correct 40% (01:35) wrong based on 83 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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Re: Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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16 Feb 2017, 00:04
1
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 ----> $$8 + 1 = 9$$

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Joined: 02 Aug 2009
Posts: 7200
Re: Over the first x games of his basketball season, Martin averaged 32 po  [#permalink]

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16 Feb 2017, 02:27
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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16 Feb 2017, 10:43
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
Over the first x games of his basketball season, Martin averaged 32 po &nbs [#permalink] 16 Feb 2017, 10:43
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