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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, 09:21
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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, 10:10
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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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Re: Jack stays late after basketball practice to shoot foul shots  [#permalink]

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New post 17 Jun 2020, 00:52
how 180+.6n= .8(200+n), can someone please explain
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Re: Jack stays late after basketball practice to shoot foul shots  [#permalink]

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New post 23 Jun 2020, 04:02
Gladiator59

can you please explain : Shots scored: 180+60+x
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Re: Jack stays late after basketball practice to shoot foul shots  [#permalink]

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New post 29 Jun 2020, 07:11
Hello Subhrajyoti & VERBAL1,

1) In this equation "180+.6n= .8(200+n)", n is the number of additional shots taken after 200.

Instead of solving the problem in the manner above, you can also do something like

Let "X" be the total number of shots. From this we can derive an equation -

90% of 200 + 60% of (X - 200) = 80% (X) --> This equation is the total number of shots "hit". When you solve it for "X", you get the total shows "taken" which is 300

So, out of the 300 shots, he "hits" 240, but he decides to take "n" additional shots (all of these shots "hitting") to hit 90% of all shots. Keyword is additional here.

So basically he wants to hit --> 90% of (300 + n) = 240 + n --> n = 300

2) can you please explain : Shots scored: 180+60+x --> 180 is the shots scored [90% of 200] for the first set, 60 is the 60% of additional shots (n) he takes. If you look at the equation solved, we find n = 100. Hence, 0.6(n) = 60 and x is the additional shots he needs to take and make over the total shots of "300"

I hope this explanation clears your doubts.
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Re: Jack stays late after basketball practice to shoot foul shots   [#permalink] 29 Jun 2020, 07:11

Jack stays late after basketball practice to shoot foul shots

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