Difference between revisions of "1987 AJHSME Problems/Problem 16"

(New page: ==Problem== Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball game, so her seasonal shooting average was <math>40\% </math>. In he...)
 
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==Problem==
 
==Problem==
  
Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball game, so her seasonal shooting average was <math>40\% </math>.  In her next game, she took <math>10</math> shots and raised her seasonal shooting average to <math>50\% </math>.  How many of these <math>10</math> shots did she make?
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Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball game, so her seasonal shooting [[average]] was <math>40\% </math>.  In her next game, she took <math>10</math> shots and raised her seasonal shooting average to <math>50\% </math>.  How many of these <math>10</math> shots did she make?
  
 
<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math>
 
<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math>
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==Solution==
 
==Solution==
  
After the fourth game, she took <math>40</math> shots, <math>50\% </math> of which she made, so she made <math>40\times .5=20</math> shots.  Twelve of them were made in the first three game, so in the last game she made <math>20-12=8</math> shots.
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After the fourth game, she took <math>40</math> shots, <math>50\% </math> of which she made, so she made <math>40\times .5=20</math> shots.  Twelve of them were made in the first three games, so in the last game she made <math>20-12=8</math> shots.
  
 
<math>\boxed{\text{E}}</math>
 
<math>\boxed{\text{E}}</math>
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==See Also==
 
==See Also==
  
[[1987 AJHSME Problems]]
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{{AJHSME box|year=1987|num-b=15|num-a=17}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]

Revision as of 13:40, 30 May 2009

Problem

Joyce made $12$ of her first $30$ shots in the first three games of this basketball game, so her seasonal shooting average was $40\%$. In her next game, she took $10$ shots and raised her seasonal shooting average to $50\%$. How many of these $10$ shots did she make?

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$

Solution

After the fourth game, she took $40$ shots, $50\%$ of which she made, so she made $40\times .5=20$ shots. Twelve of them were made in the first three games, so in the last game she made $20-12=8$ shots.

$\boxed{\text{E}}$

See Also

1987 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
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All AJHSME/AMC 8 Problems and Solutions
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