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Jack stays late after basketball practice to shoot foul shots

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Jack stays late after basketball practice to shoot foul shots  [#permalink]

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New post 18 Dec 2018, 10:21
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A
B
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Difficulty:

  55% (hard)

Question Stats:

57% (02:39) correct 43% (02:28) wrong based on 16 sessions

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Jack stays late after basketball practice to shoot foul shots. One night, he made 90 percent of his first 200 shots. He then made 60 percent of his remaining shots. In total, he hit 80 percent of all shots taken. However, Jack was not pleased by this and wanted to make 90 percent of all his shots. If Jack continued shooting foul shots, what is the minimum number of shots in a row that Jack would have to make to have made 90 percent of all his shots?
A) 250
B) 300
C) 350
D) 400
E) 450

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Re: Jack stays late after basketball practice to shoot foul shots  [#permalink]

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New post 18 Dec 2018, 11:10
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So jack scored 180 out of the first 200 shots he took (90%)

If he took n more shots post the first 200, we are told he made 0.6n of them. Overall his percent shots taken is 80%

so 180 + 0.6n is 80% of 200 + n

180 + 0.6n = 0.8( 200 + n)
180 + 0.6n = 160 + 0.8n
0.2n = 20
n = 100

So Jack took 100 shots after the first 200. Jack is not happy with this! :-) So he decides to take x more shots and hit all of them in a row, until his overall percent taken climbs up to 90%

Or shots taken: 300 + x

Shots scored: 180+60+x

And shots scored is 90% of shots taken.

Hence,

240 + x = 0.9( 300 + x)
240 + x = 270 + 0.9x
0.1x = 30
x = 300

Option (B) is our choice.

Best,
Gladi

Abhi077 wrote:
Jack stays late after basketball practice to shoot foul shots. One night, he made 90 percent of his first 200 shots. He then made 60 percent of his remaining shots. In total, he hit 80 percent of all shots taken. However, Jack was not pleased by this and wanted to make 90 percent of all his shots. If Jack continued shooting foul shots, what is the minimum number of shots in a row that Jack would have to make to have made 90 percent of all his shots?
A) 250
B) 300
C) 350
D) 400
E) 450

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Regards,
Gladi



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Re: Jack stays late after basketball practice to shoot foul shots   [#permalink] 18 Dec 2018, 11:10
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