Jack stays late after basketball practice to shoot foul shots. One nig

Question

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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AB112233 · Answer

0.9*200 = 180 shots made. 180/200.

3/5 of his next lot of shots were made. M = additional shots made. N total additional shots. M/N = 3/5. 5M = 3N.

180+M/200+N = 4/5 5(180+M) = 4(200+N) 900+5M = 800+4N 5M can be substituted for 3N per equation above.

N = 100. So M = 60.

Plugging values into the previous equation, 240/300 = 4/5.

Y = additional shots in a row made.

240+Y/300+Y = 9/10.

10(240+Y) = 9(300+Y) 2400+10Y = 2700+9Y Y=300.

So answer B.

Please correct me if I'm wrong or if you have any tips for speeding up my workings.

akwenok · Answer

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?

He made 90% of his 200 shots.

0.9 * 200 = 180

He then made 60% of the remaining shots to get 80% hit rate.

(180 + 0.6x) = successful shots
(200 + x) = total shots

\frac{(180+0.6x)}{(200+x)}  = 0.8

x = 100

He wants to make it 90%, how many shots in a row he needs to hit?

\frac{(240+x)}{(300+x)}  = 0.9

x = 300

btsaami · Answer

Let's use alligation.
Case 1: when overall he hit 80% shot.
We have,

90-80/ (80-60) = x/200
x=100 So, he has made 300 total shots.

"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?"

Now, this line was little confusing for me, mostly because i didn't read the first line properly nor was aware this basketball terminology. On re-reading the first line thought it is asking for minimum number of more such throws he needs to get to 90% of 300 + more throws.
For maximum hits in minimum number of throws we can assume that he makes 100% of all the remaining shots. Then again apply alligation.

100-90/90-80 = 10/10= 1 (Since, overall hits is 90%)
As the weights are equal, we can say that Jack has made another 300 shots to get to 90% hits.

Jack stays late after basketball practice to shoot foul shots. One nig

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